Graph coloring game (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Graph coloring game" in English language version.

refsWebsite

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24doi.org

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6semanticscholar.org

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3psu.edu

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3acm.org

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3gatech.edu

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3arxiv.org

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2macalester.edu

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acm.org

dl.acm.org

Junosza-Szaniawski & Rożej (2010) Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.
Faigle et al. (1993), and implied by Junosza-Szaniawski & Rożej (2010) Faigle, Ulrich; Kern, Walter; Kierstead, Henry A.; Trotter, William T. (1993). "On the Game Chromatic Number of some Classes of Graphs" (PDF). Ars Combinatoria. 35 (17): 143–150. Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.
Sidorowicz (2007), and implied by Junosza-Szaniawski & Rożej (2010) Sidorowicz, Elżbieta (2007). "The game chromatic number and the game colouring number of cactuses". Information Processing Letters. 102 (4): 147–151. doi:10.1016/j.ipl.2006.12.003. Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.

archive-it.org

wayback.archive-it.org

Sia (2009) Sia, Charmaine (2009). "The Game Chromatic Number of Some Families of Cartesian Product Graphs" (PDF). AKCE International Journal of Graphs and Combinatorics. 6 (2): 315–327. Archived from the original (PDF) on 2011-11-14. Retrieved 2014-07-16.

arxiv.org

Dunn et al. (2014) Dunn, Charles; Larsen, Victor; Lindke, Kira; Retter, Troy; Toci, Dustin (2014). "The game chromatic number of trees and forests". arXiv:1410.5223 [math.CO].
Bradshaw (2021) Bradshaw, Peter (2021). "Graph colorings with restricted bicolored subgraphs: II. The graph coloring game". Journal of Graph Theory. 100 (2): 371–383. arXiv:2008.13275. doi:10.1002/jgt.22786. S2CID 221377336.
Charpentier & Sopena (2014), extending results of Charpentier & Sopena (2013). Charpentier, Clément; Sopena, Éric (2014). "The incidence game chromatic number of (a,d)-decomposable graphs". Journal of Discrete Algorithms. 31: 14–25. doi:10.1016/j.jda.2014.10.001. S2CID 1102795. Charpentier, Clément; Sopena, Éric (2013). "Incidence Coloring Game and Arboricity of Graphs". Combinatorial Algorithms. Lecture Notes in Computer Science. Vol. 8288. pp. 106–114. arXiv:1304.0166. doi:10.1007/978-3-642-45278-9_10. ISBN 978-3-642-45277-2. S2CID 14707501.

doi.org

Bodlaender (1991) Bodlaender, Hans L. (1991). "On the complexity of some coloring games". Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science. Vol. 484. pp. 30–40. CiteSeerX 10.1.1.18.9992. doi:10.1007/3-540-53832-1_29. ISBN 978-3-540-53832-5.
Bodlaender (1991) Bodlaender, Hans L. (1991). "On the complexity of some coloring games". Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science. Vol. 484. pp. 30–40. CiteSeerX 10.1.1.18.9992. doi:10.1007/3-540-53832-1_29. ISBN 978-3-540-53832-5.
Costa, Pessoa, Soares, Sampaio (2020) Costa, Eurinardo; Pessoa, Victor Lage; Soares, Ronan; Sampaio, Rudini (2020). "PSPACE-completeness of two graph coloring games". Theoretical Computer Science. 824–825: 36–45. doi:10.1016/j.tcs.2020.03.022. S2CID 218777459.
Dinski & Zhu (1999) Dinski, Thomas; Zhu, Xuding (1999). "A bound for the game chromatic number of graphs". Discrete Mathematics. 196 (1–3): 109–115. doi:10.1016/s0012-365x(98)00197-6.
Junosza-Szaniawski & Rożej (2010) Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.
Faigle et al. (1993), and implied by Junosza-Szaniawski & Rożej (2010) Faigle, Ulrich; Kern, Walter; Kierstead, Henry A.; Trotter, William T. (1993). "On the Game Chromatic Number of some Classes of Graphs" (PDF). Ars Combinatoria. 35 (17): 143–150. Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.
Sidorowicz (2007), and implied by Junosza-Szaniawski & Rożej (2010) Sidorowicz, Elżbieta (2007). "The game chromatic number and the game colouring number of cactuses". Information Processing Letters. 102 (4): 147–151. doi:10.1016/j.ipl.2006.12.003. Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.
Guan & Zhu (1999) Guan, D. J.; Zhu, Xuding (1999). "Game chromatic number of outerplanar graphs". Journal of Graph Theory. 30 (1): 67–70. doi:10.1002/(sici)1097-0118(199901)30:1<67::aid-jgt7>3.0.co;2-m.
Upper bound by Zhu (2008), improving previous bounds of 33 in Kierstead & Trotter (1994), 30 implied by Dinski & Zhu (1999), 19 in Zhu (1999) and 18 in Kierstead (2000). Lower bound claimed by Kierstead & Trotter (1994). See a survey dedicated to the game chromatic number of planar graphs in Bartnicki et al. (2007). Zhu, Xuding (2008). "Refined activation strategy for the marking game". Journal of Combinatorial Theory, Series B. 98 (1): 1–18. doi:10.1016/j.jctb.2007.04.004. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Dinski, Thomas; Zhu, Xuding (1999). "A bound for the game chromatic number of graphs". Discrete Mathematics. 196 (1–3): 109–115. doi:10.1016/s0012-365x(98)00197-6. Zhu, Xuding (1999). "The Game Coloring Number of Planar Graphs". Journal of Combinatorial Theory, Series B. 75 (2): 245–258. doi:10.1006/jctb.1998.1878. Kierstead, Henry A. (2000). "A Simple Competitive Graph Coloring Algorithm". Journal of Combinatorial Theory, Series B. 78 (1): 57–68. doi:10.1006/jctb.1999.1927. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Bartnicki, Tomasz; Grytczuk, Jaroslaw; Kierstead, H. A.; Zhu, Xuding (2007). "The Map-Coloring Game" (PDF). American Mathematical Monthly. 114 (9): 793–803. doi:10.1080/00029890.2007.11920471. JSTOR 27642332. S2CID 15901267.
Sekigushi (2014) Sekigushi, Yosuke (2014). "The game coloring number of planar graphs with a given girth". Discrete Mathematics. 300: 11–16. doi:10.1016/j.disc.2014.04.011.
He et al. (2002) He, Wenjie; Hou, Xiaoling; Lih, Ko-Wei; Shao, Jiating; Wang, Weifan; Zhu, Xuding (2002). "Edge-partitions of planar graphs and their game coloring numbers". Journal of Graph Theory. 41 (4): 307–311. doi:10.1002/jgt.10069. S2CID 20929383.
Raspaud & Wu (2009) Raspaud, André; Wu, Jiaojiao (2009). "Game chromatic number of toroidal grids". Information Processing Letters. 109 (21–22): 1183–1186. doi:10.1016/j.ipl.2009.08.001.
Zhu (2000) Zhu, Xuding (2000). "The game coloring number of pseudo partial k-trees". Discrete Mathematics. 215 (1–3): 245–262. doi:10.1016/s0012-365x(99)00237-x.
Peterin (2007) Peterin, Iztok (2007). "Game chromatic number of Cartesian product graphs". Electronic Notes in Discrete Mathematics. 29: 353–357. CiteSeerX 10.1.1.107.111. doi:10.1016/j.endm.2007.07.060.
Bradshaw (2021) Bradshaw, Peter (2021). "Graph colorings with restricted bicolored subgraphs: II. The graph coloring game". Journal of Graph Theory. 100 (2): 371–383. arXiv:2008.13275. doi:10.1002/jgt.22786. S2CID 221377336.
Zhu (1999) Zhu, Xuding (1999). "The Game Coloring Number of Planar Graphs". Journal of Combinatorial Theory, Series B. 75 (2): 245–258. doi:10.1006/jctb.1998.1878.
Beveridge et al. (2008) Beveridge, Andrew; Bohman, Tom; Friezeb, Alan; Pikhurko, Oleg (2008). "Game chromatic index of graphs with given restrictions on degrees". Theoretical Computer Science. 407 (1–3): 242–249. doi:10.1016/j.tcs.2008.05.026.
Bartnicki & Grytczuk (2008), improving results on k-degenerate graphs in Cai & Zhu (2001) Bartnicki, Tomasz; Grytczuk, Jarosław (2008). "A Note on the Game Chromatic Index of Graphs". Graphs and Combinatorics. 24 (2): 67–70. doi:10.1007/s00373-008-0774-z. S2CID 19373685. Cai, Leizhen; Zhu, Xuding (2001). "Game Chromatic Index of k-Degenerate Graphs". Journal of Graph Theory. 36 (3): 144–155. doi:10.1002/1097-0118(200103)36:3<144::aid-jgt1002>3.0.co;2-f.
Upper bound of Δ+2 by Lam, Shiu & Xu (1999), then bound of Δ+1 by Erdös et al. (2004) for cases Δ=3 and Δ≥6, and by Andres (2006) for case Δ=5. Lam, Peter C. B.; Shiu, Wai C.; Xu, Baogang (1999). "Edge game coloring of graphs" (PDF). Graph Theory Notes N.Y. 37: 17–19. Erdös, Peter L.; Faigle, Ulrich; Hochstättler, Winfried; Kern, Walter (2004). "Note on the game chromatic index of trees". Theoretical Computer Science. 313 (3): 371–376. doi:10.1016/j.tcs.2002.10.002. Andres, Stephan D. (2006). "The game chromatic index of forests of maximum degree Δ ⩾ 5". Discrete Applied Mathematics. 154 (9): 1317–1323. doi:10.1016/j.dam.2005.05.031.
Conditions on forests with Δ=4 are in Chan & Nong (2014) Chan, Wai H.; Nong, Ge (2014). "The game chromatic index of some trees of maximum degree 4". Discrete Applied Mathematics. 170: 1–6. doi:10.1016/j.dam.2014.01.003.
Andres (2009a), see also erratum in Andres (2009b) Andres, Stefan D. (2009). "The incidence game chromatic number". Discrete Applied Mathematics. 157 (9): 1980–1987. doi:10.1016/j.dam.2007.10.021. Andres, Stefan D. (2009). "Erratum to: The incidence game chromatic number". Discrete Applied Mathematics. 158 (6): 728. doi:10.1016/j.dam.2009.11.017.
Charpentier & Sopena (2014), extending results of Charpentier & Sopena (2013). Charpentier, Clément; Sopena, Éric (2014). "The incidence game chromatic number of (a,d)-decomposable graphs". Journal of Discrete Algorithms. 31: 14–25. doi:10.1016/j.jda.2014.10.001. S2CID 1102795. Charpentier, Clément; Sopena, Éric (2013). "Incidence Coloring Game and Arboricity of Graphs". Combinatorial Algorithms. Lecture Notes in Computer Science. Vol. 8288. pp. 106–114. arXiv:1304.0166. doi:10.1007/978-3-642-45278-9_10. ISBN 978-3-642-45277-2. S2CID 14707501.
Kim (2011), improving a similar result for k ≥ 7 in Andres (2009a) (see also erratum in Andres (2009b)) Kim, John Y. (2011). "The incidence game chromatic number of paths and subgraphs of wheels". Discrete Applied Mathematics. 159 (8): 683–694. doi:10.1016/j.dam.2010.01.001. Andres, Stefan D. (2009). "The incidence game chromatic number". Discrete Applied Mathematics. 157 (9): 1980–1987. doi:10.1016/j.dam.2007.10.021. Andres, Stefan D. (2009). "Erratum to: The incidence game chromatic number". Discrete Applied Mathematics. 158 (6): 728. doi:10.1016/j.dam.2009.11.017.
Kim (2011) Kim, John Y. (2011). "The incidence game chromatic number of paths and subgraphs of wheels". Discrete Applied Mathematics. 159 (8): 683–694. doi:10.1016/j.dam.2010.01.001.

gatech.edu

people.math.gatech.edu

Faigle et al. (1993), and implied by Junosza-Szaniawski & Rożej (2010) Faigle, Ulrich; Kern, Walter; Kierstead, Henry A.; Trotter, William T. (1993). "On the Game Chromatic Number of some Classes of Graphs" (PDF). Ars Combinatoria. 35 (17): 143–150. Junosza-Szaniawski, Konstanty; Rożej, Łukasz (2010). "Game chromatic number of graphs with locally bounded number of cycles". Information Processing Letters. 110 (17): 757–760. doi:10.1016/j.ipl.2010.06.004.
Upper bound by Zhu (2008), improving previous bounds of 33 in Kierstead & Trotter (1994), 30 implied by Dinski & Zhu (1999), 19 in Zhu (1999) and 18 in Kierstead (2000). Lower bound claimed by Kierstead & Trotter (1994). See a survey dedicated to the game chromatic number of planar graphs in Bartnicki et al. (2007). Zhu, Xuding (2008). "Refined activation strategy for the marking game". Journal of Combinatorial Theory, Series B. 98 (1): 1–18. doi:10.1016/j.jctb.2007.04.004. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Dinski, Thomas; Zhu, Xuding (1999). "A bound for the game chromatic number of graphs". Discrete Mathematics. 196 (1–3): 109–115. doi:10.1016/s0012-365x(98)00197-6. Zhu, Xuding (1999). "The Game Coloring Number of Planar Graphs". Journal of Combinatorial Theory, Series B. 75 (2): 245–258. doi:10.1006/jctb.1998.1878. Kierstead, Henry A. (2000). "A Simple Competitive Graph Coloring Algorithm". Journal of Combinatorial Theory, Series B. 78 (1): 57–68. doi:10.1006/jctb.1999.1927. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Bartnicki, Tomasz; Grytczuk, Jaroslaw; Kierstead, H. A.; Zhu, Xuding (2007). "The Map-Coloring Game" (PDF). American Mathematical Monthly. 114 (9): 793–803. doi:10.1080/00029890.2007.11920471. JSTOR 27642332. S2CID 15901267.
Faigle et al. (1993) Faigle, Ulrich; Kern, Walter; Kierstead, Henry A.; Trotter, William T. (1993). "On the Game Chromatic Number of some Classes of Graphs" (PDF). Ars Combinatoria. 35 (17): 143–150.

harvard.edu

math.harvard.edu

Sia (2009) Sia, Charmaine (2009). "The Game Chromatic Number of Some Families of Cartesian Product Graphs" (PDF). AKCE International Journal of Graphs and Combinatorics. 6 (2): 315–327. Archived from the original (PDF) on 2011-11-14. Retrieved 2014-07-16.

jstor.org

Upper bound by Zhu (2008), improving previous bounds of 33 in Kierstead & Trotter (1994), 30 implied by Dinski & Zhu (1999), 19 in Zhu (1999) and 18 in Kierstead (2000). Lower bound claimed by Kierstead & Trotter (1994). See a survey dedicated to the game chromatic number of planar graphs in Bartnicki et al. (2007). Zhu, Xuding (2008). "Refined activation strategy for the marking game". Journal of Combinatorial Theory, Series B. 98 (1): 1–18. doi:10.1016/j.jctb.2007.04.004. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Dinski, Thomas; Zhu, Xuding (1999). "A bound for the game chromatic number of graphs". Discrete Mathematics. 196 (1–3): 109–115. doi:10.1016/s0012-365x(98)00197-6. Zhu, Xuding (1999). "The Game Coloring Number of Planar Graphs". Journal of Combinatorial Theory, Series B. 75 (2): 245–258. doi:10.1006/jctb.1998.1878. Kierstead, Henry A. (2000). "A Simple Competitive Graph Coloring Algorithm". Journal of Combinatorial Theory, Series B. 78 (1): 57–68. doi:10.1006/jctb.1999.1927. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Bartnicki, Tomasz; Grytczuk, Jaroslaw; Kierstead, H. A.; Zhu, Xuding (2007). "The Map-Coloring Game" (PDF). American Mathematical Monthly. 114 (9): 793–803. doi:10.1080/00029890.2007.11920471. JSTOR 27642332. S2CID 15901267.

macalester.edu

Lam, Shiu & Xu (1999) Lam, Peter C. B.; Shiu, Wai C.; Xu, Baogang (1999). "Edge game coloring of graphs" (PDF). Graph Theory Notes N.Y. 37: 17–19.
Upper bound of Δ+2 by Lam, Shiu & Xu (1999), then bound of Δ+1 by Erdös et al. (2004) for cases Δ=3 and Δ≥6, and by Andres (2006) for case Δ=5. Lam, Peter C. B.; Shiu, Wai C.; Xu, Baogang (1999). "Edge game coloring of graphs" (PDF). Graph Theory Notes N.Y. 37: 17–19. Erdös, Peter L.; Faigle, Ulrich; Hochstättler, Winfried; Kern, Walter (2004). "Note on the game chromatic index of trees". Theoretical Computer Science. 313 (3): 371–376. doi:10.1016/j.tcs.2002.10.002. Andres, Stephan D. (2006). "The game chromatic index of forests of maximum degree Δ ⩾ 5". Discrete Applied Mathematics. 154 (9): 1317–1323. doi:10.1016/j.dam.2005.05.031.

psu.edu

citeseerx.ist.psu.edu

Bodlaender (1991) Bodlaender, Hans L. (1991). "On the complexity of some coloring games". Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science. Vol. 484. pp. 30–40. CiteSeerX 10.1.1.18.9992. doi:10.1007/3-540-53832-1_29. ISBN 978-3-540-53832-5.
Bodlaender (1991) Bodlaender, Hans L. (1991). "On the complexity of some coloring games". Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science. Vol. 484. pp. 30–40. CiteSeerX 10.1.1.18.9992. doi:10.1007/3-540-53832-1_29. ISBN 978-3-540-53832-5.
Peterin (2007) Peterin, Iztok (2007). "Game chromatic number of Cartesian product graphs". Electronic Notes in Discrete Mathematics. 29: 353–357. CiteSeerX 10.1.1.107.111. doi:10.1016/j.endm.2007.07.060.

semanticscholar.org

api.semanticscholar.org

Costa, Pessoa, Soares, Sampaio (2020) Costa, Eurinardo; Pessoa, Victor Lage; Soares, Ronan; Sampaio, Rudini (2020). "PSPACE-completeness of two graph coloring games". Theoretical Computer Science. 824–825: 36–45. doi:10.1016/j.tcs.2020.03.022. S2CID 218777459.
Upper bound by Zhu (2008), improving previous bounds of 33 in Kierstead & Trotter (1994), 30 implied by Dinski & Zhu (1999), 19 in Zhu (1999) and 18 in Kierstead (2000). Lower bound claimed by Kierstead & Trotter (1994). See a survey dedicated to the game chromatic number of planar graphs in Bartnicki et al. (2007). Zhu, Xuding (2008). "Refined activation strategy for the marking game". Journal of Combinatorial Theory, Series B. 98 (1): 1–18. doi:10.1016/j.jctb.2007.04.004. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Dinski, Thomas; Zhu, Xuding (1999). "A bound for the game chromatic number of graphs". Discrete Mathematics. 196 (1–3): 109–115. doi:10.1016/s0012-365x(98)00197-6. Zhu, Xuding (1999). "The Game Coloring Number of Planar Graphs". Journal of Combinatorial Theory, Series B. 75 (2): 245–258. doi:10.1006/jctb.1998.1878. Kierstead, Henry A. (2000). "A Simple Competitive Graph Coloring Algorithm". Journal of Combinatorial Theory, Series B. 78 (1): 57–68. doi:10.1006/jctb.1999.1927. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Bartnicki, Tomasz; Grytczuk, Jaroslaw; Kierstead, H. A.; Zhu, Xuding (2007). "The Map-Coloring Game" (PDF). American Mathematical Monthly. 114 (9): 793–803. doi:10.1080/00029890.2007.11920471. JSTOR 27642332. S2CID 15901267.
He et al. (2002) He, Wenjie; Hou, Xiaoling; Lih, Ko-Wei; Shao, Jiating; Wang, Weifan; Zhu, Xuding (2002). "Edge-partitions of planar graphs and their game coloring numbers". Journal of Graph Theory. 41 (4): 307–311. doi:10.1002/jgt.10069. S2CID 20929383.
Bradshaw (2021) Bradshaw, Peter (2021). "Graph colorings with restricted bicolored subgraphs: II. The graph coloring game". Journal of Graph Theory. 100 (2): 371–383. arXiv:2008.13275. doi:10.1002/jgt.22786. S2CID 221377336.
Bartnicki & Grytczuk (2008), improving results on k-degenerate graphs in Cai & Zhu (2001) Bartnicki, Tomasz; Grytczuk, Jarosław (2008). "A Note on the Game Chromatic Index of Graphs". Graphs and Combinatorics. 24 (2): 67–70. doi:10.1007/s00373-008-0774-z. S2CID 19373685. Cai, Leizhen; Zhu, Xuding (2001). "Game Chromatic Index of k-Degenerate Graphs". Journal of Graph Theory. 36 (3): 144–155. doi:10.1002/1097-0118(200103)36:3<144::aid-jgt1002>3.0.co;2-f.
Charpentier & Sopena (2014), extending results of Charpentier & Sopena (2013). Charpentier, Clément; Sopena, Éric (2014). "The incidence game chromatic number of (a,d)-decomposable graphs". Journal of Discrete Algorithms. 31: 14–25. doi:10.1016/j.jda.2014.10.001. S2CID 1102795. Charpentier, Clément; Sopena, Éric (2013). "Incidence Coloring Game and Arboricity of Graphs". Combinatorial Algorithms. Lecture Notes in Computer Science. Vol. 8288. pp. 106–114. arXiv:1304.0166. doi:10.1007/978-3-642-45278-9_10. ISBN 978-3-642-45277-2. S2CID 14707501.

umd.edu

cs.umd.edu

Upper bound by Zhu (2008), improving previous bounds of 33 in Kierstead & Trotter (1994), 30 implied by Dinski & Zhu (1999), 19 in Zhu (1999) and 18 in Kierstead (2000). Lower bound claimed by Kierstead & Trotter (1994). See a survey dedicated to the game chromatic number of planar graphs in Bartnicki et al. (2007). Zhu, Xuding (2008). "Refined activation strategy for the marking game". Journal of Combinatorial Theory, Series B. 98 (1): 1–18. doi:10.1016/j.jctb.2007.04.004. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Dinski, Thomas; Zhu, Xuding (1999). "A bound for the game chromatic number of graphs". Discrete Mathematics. 196 (1–3): 109–115. doi:10.1016/s0012-365x(98)00197-6. Zhu, Xuding (1999). "The Game Coloring Number of Planar Graphs". Journal of Combinatorial Theory, Series B. 75 (2): 245–258. doi:10.1006/jctb.1998.1878. Kierstead, Henry A. (2000). "A Simple Competitive Graph Coloring Algorithm". Journal of Combinatorial Theory, Series B. 78 (1): 57–68. doi:10.1006/jctb.1999.1927. Kierstead, Henry A.; Trotter, William T. (1994). "Planar Graph Coloring with an Uncooperative Partner" (PDF). Journal of Graph Theory. 18 (6): 564–584. doi:10.1002/jgt.3190180605. Bartnicki, Tomasz; Grytczuk, Jaroslaw; Kierstead, H. A.; Zhu, Xuding (2007). "The Map-Coloring Game" (PDF). American Mathematical Monthly. 114 (9): 793–803. doi:10.1080/00029890.2007.11920471. JSTOR 27642332. S2CID 15901267.

utwente.nl

research.utwente.nl

Upper bound of Δ+2 by Lam, Shiu & Xu (1999), then bound of Δ+1 by Erdös et al. (2004) for cases Δ=3 and Δ≥6, and by Andres (2006) for case Δ=5. Lam, Peter C. B.; Shiu, Wai C.; Xu, Baogang (1999). "Edge game coloring of graphs" (PDF). Graph Theory Notes N.Y. 37: 17–19. Erdös, Peter L.; Faigle, Ulrich; Hochstättler, Winfried; Kern, Walter (2004). "Note on the game chromatic index of trees". Theoretical Computer Science. 313 (3): 371–376. doi:10.1016/j.tcs.2002.10.002. Andres, Stephan D. (2006). "The game chromatic index of forests of maximum degree Δ ⩾ 5". Discrete Applied Mathematics. 154 (9): 1317–1323. doi:10.1016/j.dam.2005.05.031.