Circle graph (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Circle graph" in English language version.

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12doi.org

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3arxiv.org

69^th place

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2ams.org

451^st place

277^th place

2semanticscholar.org

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8^th place

1graphclasses.org

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ams.org

mathscinet.ams.org

Davies & McCarty (2021). For earlier bounds see Černý (2007), Gyárfás (1985), Kostochka (1988), and Kostochka & Kratochvíl (1997). Davies, James; McCarty, Rose (2021), "Circle graphs are quadratically χ-bounded", Bulletin of the London Mathematical Society, 53 (3): 673–679, arXiv:1905.11578, doi:10.1112/blms.12447, MR 4275079, S2CID 167217723. Černý, Jakub (2007), "Coloring circle graphs", Electronic Notes in Discrete Mathematics, 29: 357–361, doi:10.1016/j.endm.2007.07.072. Gyárfás, A. (1985), "On the chromatic number of multiple interval graphs and overlap graphs", Discrete Mathematics, 55 (2): 161–166, doi:10.1016/0012-365X(85)90044-5. As cited by Ageev (1996). Kostochka, A.V. (1988), "Upper bounds on the chromatic number of graphs", Trudy Instituta Mathematiki (in Russian), 10: 204–226, MR 0945704. As cited by Ageev (1996). Kostochka, A.V.; Kratochvíl, J. (1997), "Covering and coloring polygon-circle graphs", Discrete Mathematics, 163 (1–3): 299–305, doi:10.1016/S0012-365X(96)00344-5.
See Kostochka (1988) for the upper bound, and Ageev (1996) for the matching lower bound. Karapetyan (1984) and Gyárfás & Lehel (1985) give earlier weaker bounds on the same problem. Kostochka, A.V. (1988), "Upper bounds on the chromatic number of graphs", Trudy Instituta Mathematiki (in Russian), 10: 204–226, MR 0945704. As cited by Ageev (1996). Ageev, A. A. (1996), "A triangle-free circle graph with chromatic number 5", Discrete Mathematics, 152 (1–3): 295–298, doi:10.1016/0012-365X(95)00349-2. Karapetyan, A. (1984), On perfect arc and chord intersection graphs, Ph.D. thesis (in Russian), Inst. of Mathematics, Novosibirsk. As cited by Ageev (1996). Gyárfás, A.; Lehel, J. (1985), "Covering and coloring problems for relatives of intervals", Discrete Mathematics, 55 (2): 167–180, doi:10.1016/0012-365X(85)90045-7. As cited by Ageev (1996).

arxiv.org

Gioan et al. (2013). Gioan, Emeric; Paul, Christophe; Tedder, Marc; Corneil, Derek (March 2013), "Practical and efficient circle graph recognition", Algorithmica, 69 (4): 759–788, arXiv:1104.3284, doi:10.1007/s00453-013-9745-8
Davies & McCarty (2021). For earlier bounds see Černý (2007), Gyárfás (1985), Kostochka (1988), and Kostochka & Kratochvíl (1997). Davies, James; McCarty, Rose (2021), "Circle graphs are quadratically χ-bounded", Bulletin of the London Mathematical Society, 53 (3): 673–679, arXiv:1905.11578, doi:10.1112/blms.12447, MR 4275079, S2CID 167217723. Černý, Jakub (2007), "Coloring circle graphs", Electronic Notes in Discrete Mathematics, 29: 357–361, doi:10.1016/j.endm.2007.07.072. Gyárfás, A. (1985), "On the chromatic number of multiple interval graphs and overlap graphs", Discrete Mathematics, 55 (2): 161–166, doi:10.1016/0012-365X(85)90044-5. As cited by Ageev (1996). Kostochka, A.V. (1988), "Upper bounds on the chromatic number of graphs", Trudy Instituta Mathematiki (in Russian), 10: 204–226, MR 0945704. As cited by Ageev (1996). Kostochka, A.V.; Kratochvíl, J. (1997), "Covering and coloring polygon-circle graphs", Discrete Mathematics, 163 (1–3): 299–305, doi:10.1016/S0012-365X(96)00344-5.
Bandelt, Chepoi & Eppstein (2010). Bandelt, H.-J.; Chepoi, V.; Eppstein, D. (2010), "Combinatorics and geometry of finite and infinite squaregraphs", SIAM Journal on Discrete Mathematics, 24 (4): 1399–1440, arXiv:0905.4537, doi:10.1137/090760301, S2CID 10788524.

doi.org

Gabor, Supowit & Hsu (1989); Spinrad (1994) Gabor, Csaba P.; Supowit, Kenneth J.; Hsu, Wen-Lian (July 1989), "Recognizing circle graphs in polynomial time", Journal of the ACM, 36 (3): 435–473, doi:10.1145/65950.65951 Spinrad, Jeremy (1994), "Recognition of circle graphs", Journal of Algorithms, 16 (2): 264–282, doi:10.1006/jagm.1994.1012.
Gioan et al. (2013). Gioan, Emeric; Paul, Christophe; Tedder, Marc; Corneil, Derek (March 2013), "Practical and efficient circle graph recognition", Algorithmica, 69 (4): 759–788, arXiv:1104.3284, doi:10.1007/s00453-013-9745-8
Kloks, Kratsch & Wong (1998). Kloks, T.; Kratsch, D.; Wong, C. K. (1998), "Minimum fill-in on circle and circular-arc graphs", Journal of Algorithms, 28 (2): 272–289, doi:10.1006/jagm.1998.0936.
Keil (1993) Keil, J. Mark (1993), "The complexity of domination problems in circle graphs", Discrete Applied Mathematics, 42 (1): 51–63, doi:10.1016/0166-218X(93)90178-Q.
Garey et al. (1980). Garey, M. R.; Johnson, D. S.; Miller, G. L.; Papadimitriou, C. (1980), "The complexity of coloring circular arcs and chords", SIAM Journal on Algebraic and Discrete Methods, 1 (2): 216–227, doi:10.1137/0601025
Unger (1988). Unger, Walter (1988), "On the k-colouring of circle-graphs", STACS 88: 5th Annual Symposium on Theoretical Aspects of Computer Science, Bordeaux, France, February 11–13, 1988, Proceedings, Lecture Notes in Computer Science, vol. 294, Berlin: Springer, pp. 61–72, doi:10.1007/BFb0035832.
Unger (1992). Unger, Walter (1992), "The complexity of colouring circle graphs", STACS 92: 9th Annual Symposium on Theoretical Aspects of Computer Science, Cachan, France, February 13–15, 1992, Proceedings, Lecture Notes in Computer Science, vol. 577, Berlin: Springer, pp. 389–400, doi:10.1007/3-540-55210-3_199.
Davies & McCarty (2021). For earlier bounds see Černý (2007), Gyárfás (1985), Kostochka (1988), and Kostochka & Kratochvíl (1997). Davies, James; McCarty, Rose (2021), "Circle graphs are quadratically χ-bounded", Bulletin of the London Mathematical Society, 53 (3): 673–679, arXiv:1905.11578, doi:10.1112/blms.12447, MR 4275079, S2CID 167217723. Černý, Jakub (2007), "Coloring circle graphs", Electronic Notes in Discrete Mathematics, 29: 357–361, doi:10.1016/j.endm.2007.07.072. Gyárfás, A. (1985), "On the chromatic number of multiple interval graphs and overlap graphs", Discrete Mathematics, 55 (2): 161–166, doi:10.1016/0012-365X(85)90044-5. As cited by Ageev (1996). Kostochka, A.V. (1988), "Upper bounds on the chromatic number of graphs", Trudy Instituta Mathematiki (in Russian), 10: 204–226, MR 0945704. As cited by Ageev (1996). Kostochka, A.V.; Kratochvíl, J. (1997), "Covering and coloring polygon-circle graphs", Discrete Mathematics, 163 (1–3): 299–305, doi:10.1016/S0012-365X(96)00344-5.
See Kostochka (1988) for the upper bound, and Ageev (1996) for the matching lower bound. Karapetyan (1984) and Gyárfás & Lehel (1985) give earlier weaker bounds on the same problem. Kostochka, A.V. (1988), "Upper bounds on the chromatic number of graphs", Trudy Instituta Mathematiki (in Russian), 10: 204–226, MR 0945704. As cited by Ageev (1996). Ageev, A. A. (1996), "A triangle-free circle graph with chromatic number 5", Discrete Mathematics, 152 (1–3): 295–298, doi:10.1016/0012-365X(95)00349-2. Karapetyan, A. (1984), On perfect arc and chord intersection graphs, Ph.D. thesis (in Russian), Inst. of Mathematics, Novosibirsk. As cited by Ageev (1996). Gyárfás, A.; Lehel, J. (1985), "Covering and coloring problems for relatives of intervals", Discrete Mathematics, 55 (2): 167–180, doi:10.1016/0012-365X(85)90045-7. As cited by Ageev (1996).
Ageev (1999). Ageev, A. A. (1999), "Every circle graph of girth at least 5 is 3-colourable", Discrete Mathematics, 195 (1–3): 229–233, doi:10.1016/S0012-365X(98)00192-7.
Bandelt, Chepoi & Eppstein (2010). Bandelt, H.-J.; Chepoi, V.; Eppstein, D. (2010), "Combinatorics and geometry of finite and infinite squaregraphs", SIAM Journal on Discrete Mathematics, 24 (4): 1399–1440, arXiv:0905.4537, doi:10.1137/090760301, S2CID 10788524.
Wessel & Pöschel (1985); Unger (1988). Wessel, W.; Pöschel, R. (1985), "On circle graphs", in Sachs, Horst (ed.), Graphs, Hypergraphs and Applications: Proceedings of the Conference on Graph Theory Held in Eyba, October 1st to 5th, 1984, Teubner-Texte zur Mathematik, vol. 73, B.G. Teubner, pp. 207–210. As cited by Unger (1988). Unger, Walter (1988), "On the k-colouring of circle-graphs", STACS 88: 5th Annual Symposium on Theoretical Aspects of Computer Science, Bordeaux, France, February 11–13, 1988, Proceedings, Lecture Notes in Computer Science, vol. 294, Berlin: Springer, pp. 61–72, doi:10.1007/BFb0035832.

graphclasses.org

"Circle graph", Information System on Graph Classes and their Inclusions

semanticscholar.org

api.semanticscholar.org

Davies & McCarty (2021). For earlier bounds see Černý (2007), Gyárfás (1985), Kostochka (1988), and Kostochka & Kratochvíl (1997). Davies, James; McCarty, Rose (2021), "Circle graphs are quadratically χ-bounded", Bulletin of the London Mathematical Society, 53 (3): 673–679, arXiv:1905.11578, doi:10.1112/blms.12447, MR 4275079, S2CID 167217723. Černý, Jakub (2007), "Coloring circle graphs", Electronic Notes in Discrete Mathematics, 29: 357–361, doi:10.1016/j.endm.2007.07.072. Gyárfás, A. (1985), "On the chromatic number of multiple interval graphs and overlap graphs", Discrete Mathematics, 55 (2): 161–166, doi:10.1016/0012-365X(85)90044-5. As cited by Ageev (1996). Kostochka, A.V. (1988), "Upper bounds on the chromatic number of graphs", Trudy Instituta Mathematiki (in Russian), 10: 204–226, MR 0945704. As cited by Ageev (1996). Kostochka, A.V.; Kratochvíl, J. (1997), "Covering and coloring polygon-circle graphs", Discrete Mathematics, 163 (1–3): 299–305, doi:10.1016/S0012-365X(96)00344-5.
Bandelt, Chepoi & Eppstein (2010). Bandelt, H.-J.; Chepoi, V.; Eppstein, D. (2010), "Combinatorics and geometry of finite and infinite squaregraphs", SIAM Journal on Discrete Mathematics, 24 (4): 1399–1440, arXiv:0905.4537, doi:10.1137/090760301, S2CID 10788524.