Branch-decomposition (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Branch-decomposition" in English language version.

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15doi.org

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Oum & Seymour (2007). Oum, Sang-il; Seymour, Paul (2007), "Testing branch-width", Journal of Combinatorial Theory, Series B, 97 (3): 385–393, doi:10.1016/j.jctb.2006.06.006, MR 2305892.

archives-ouvertes.fr

hal.archives-ouvertes.fr

Bodlaender & Thilikos (1997). Fomin, Mazoit & Todinca (2009) describe an algorithm with improved dependence on k, (2√3)^k, at the expense of an increase in the dependence on the number of vertices from linear to quadratic. Bodlaender, Hans L.; Thilikos, Dimitrios M. (1997), "Constructive linear time algorithms for branchwidth", Proc. 24th International Colloquium on Automata, Languages and Programming (ICALP '97), Lecture Notes in Computer Science, vol. 1256, Springer-Verlag, pp. 627–637, doi:10.1007/3-540-63165-8_217, hdl:2117/96447, ISBN 978-3-540-63165-1. Fomin, Fedor V.; Mazoit, Frédéric; Todinca, Ioan (2009), "Computing branchwidth via efficient triangulations and blocks", Discrete Applied Mathematics, 157 (12): 2726–2736, doi:10.1016/j.dam.2008.08.009.
Mazoit & Thomassé (2007). Mazoit, Frédéric; Thomassé, Stéphan (2007), "Branchwidth of graphic matroids", in Hilton, Anthony; Talbot, John (eds.), Surveys in Combinatorics 2007 (PDF), London Mathematical Society Lecture Note Series, vol. 346, Cambridge University Press, p. 275.
Mazoit & Thomassé (2007); Hicks & McMurray (2007). Mazoit, Frédéric; Thomassé, Stéphan (2007), "Branchwidth of graphic matroids", in Hilton, Anthony; Talbot, John (eds.), Surveys in Combinatorics 2007 (PDF), London Mathematical Society Lecture Note Series, vol. 346, Cambridge University Press, p. 275. Hicks, Illya V.; McMurray, Nolan B. Jr. (2007), "The branchwidth of graphs and their cycle matroids", Journal of Combinatorial Theory, Series B, 97 (5): 681–692, doi:10.1016/j.jctb.2006.12.007.

books.google.com

Kao, Ming-Yang, ed. (2008), "Treewidth of graphs", Encyclopedia of Algorithms, Springer, p. 969, ISBN 9780387307701, Another long-standing open problem is whether there is a polynomial-time algorithm to compute the treewidth of planar graphs.

doi.org

Robertson & Seymour 1991, Theorem 5.1, p. 168. Robertson, Neil; Seymour, Paul D. (1991), "Graph minors. X. Obstructions to tree-decomposition", Journal of Combinatorial Theory, 52 (2): 153–190, doi:10.1016/0095-8956(91)90061-N.
Seymour & Thomas (1994). Seymour, Paul D.; Thomas, Robin (1994), "Call routing and the ratcatcher", Combinatorica, 14 (2): 217–241, doi:10.1007/BF01215352.
Robertson & Seymour (1991), Theorem 4.1, p. 164. Robertson, Neil; Seymour, Paul D. (1991), "Graph minors. X. Obstructions to tree-decomposition", Journal of Combinatorial Theory, 52 (2): 153–190, doi:10.1016/0095-8956(91)90061-N.
Bodlaender & Thilikos (1997). Fomin, Mazoit & Todinca (2009) describe an algorithm with improved dependence on k, (2√3)^k, at the expense of an increase in the dependence on the number of vertices from linear to quadratic. Bodlaender, Hans L.; Thilikos, Dimitrios M. (1997), "Constructive linear time algorithms for branchwidth", Proc. 24th International Colloquium on Automata, Languages and Programming (ICALP '97), Lecture Notes in Computer Science, vol. 1256, Springer-Verlag, pp. 627–637, doi:10.1007/3-540-63165-8_217, hdl:2117/96447, ISBN 978-3-540-63165-1. Fomin, Fedor V.; Mazoit, Frédéric; Todinca, Ioan (2009), "Computing branchwidth via efficient triangulations and blocks", Discrete Applied Mathematics, 157 (12): 2726–2736, doi:10.1016/j.dam.2008.08.009.
Gu & Tamaki (2008). Gu, Qian-Ping; Tamaki, Hisao (July 2008), "Optimal branch-decomposition of planar graphs in O(n³) time", ACM Transactions on Algorithms, 4 (3): 30:1–30:13, doi:10.1145/1367064.1367070.
Hicks (2000); Hliněný (2003). Hicks, Illya V. (2000), Branch Decompositions and their Applications, Ph.D. thesis, Rice University, archived from the original on 2011-07-16, retrieved 2010-07-06. Hliněný, Petr (2003), "On matroid properties definable in the MSO logic", Proc. 28th International Symposium on Mathematical Foundations of Computer Science (MFCS '03), Lecture Notes in Computer Science, vol. 2747, Springer-Verlag, pp. 470–479, doi:10.1007/978-3-540-45138-9\_41 (inactive 1 November 2024){{citation}}: CS1 maint: DOI inactive as of November 2024 (link)
Robertson & Seymour 1991. Section 12, "Tangles and Matroids", pp. 188–190. Robertson, Neil; Seymour, Paul D. (1991), "Graph minors. X. Obstructions to tree-decomposition", Journal of Combinatorial Theory, 52 (2): 153–190, doi:10.1016/0095-8956(91)90061-N.
Mazoit & Thomassé (2007); Hicks & McMurray (2007). Mazoit, Frédéric; Thomassé, Stéphan (2007), "Branchwidth of graphic matroids", in Hilton, Anthony; Talbot, John (eds.), Surveys in Combinatorics 2007 (PDF), London Mathematical Society Lecture Note Series, vol. 346, Cambridge University Press, p. 275. Hicks, Illya V.; McMurray, Nolan B. Jr. (2007), "The branchwidth of graphs and their cycle matroids", Journal of Combinatorial Theory, Series B, 97 (5): 681–692, doi:10.1016/j.jctb.2006.12.007.
Hliněný & Whittle (2006). Hliněný, Petr; Whittle, Geoff (2006), "Matroid tree-width" (PDF), European Journal of Combinatorics, 27 (7): 1117–1128, doi:10.1016/j.ejc.2006.06.005, archived from the original (PDF) on 2012-03-06, retrieved 2010-07-06.
- Geelen, Gerards & Whittle (2002); Geelen, Gerards & Whittle (2006). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2002), "Branch-width and well-quasi-ordering in matroids and graphs", Journal of Combinatorial Theory, Series B, 84 (2): 270–290, doi:10.1006/jctb.2001.2082. Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842.
- Geelen, Gerards & Whittle (2006); Geelen, Gerards & Whittle (2007). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842. Geelen, Jim; Gerards, Bert; Whittle, Geoff (2007), "Excluding a planar graph from GF(q)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 97 (6): 971–998, doi:10.1016/j.jctb.2007.02.005, archived from the original (PDF) on 2010-09-24.
- Oum & Seymour (2007). Oum, Sang-il; Seymour, Paul (2007), "Testing branch-width", Journal of Combinatorial Theory, Series B, 97 (3): 385–393, doi:10.1016/j.jctb.2006.06.006, MR 2305892.
- Robertson & Seymour (1991), Theorem 4.2, p. 165. Robertson, Neil; Seymour, Paul D. (1991), "Graph minors. X. Obstructions to tree-decomposition", Journal of Combinatorial Theory, 52 (2): 153–190, doi:10.1016/0095-8956(91)90061-N.
- Bodlaender & Thilikos (1999). The fourth forbidden minor for treewidth three, the pentagonal prism, has the cube graph as a minor, so it is not minimal for branchwidth three. Bodlaender, Hans L.; Thilikos, Dimitrios M. (1999), "Graphs with branchwidth at most three", Journal of Algorithms, 32 (2): 167–194, doi:10.1006/jagm.1999.1011.
- Hall et al. (2002); Geelen et al. (2003). Hall, Rhiannon; Oxley, James; Semple, Charles; Whittle, Geoff (2002), "On matroids of branch-width three", Journal of Combinatorial Theory, Series B, 86 (1): 148–171, doi:10.1006/jctb.2002.2120. Geelen, Jim; Gerards, Bert; Robertson, Neil; Whittle, Geoff (2003), "On the excluded minors for the matroids of branch-width k", Journal of Combinatorial Theory, Series B, 88 (2): 261–265, doi:10.1016/S0095-8956(02)00046-1.

handle.net

hdl.handle.net

Bodlaender & Thilikos (1997). Fomin, Mazoit & Todinca (2009) describe an algorithm with improved dependence on k, (2√3)^k, at the expense of an increase in the dependence on the number of vertices from linear to quadratic. Bodlaender, Hans L.; Thilikos, Dimitrios M. (1997), "Constructive linear time algorithms for branchwidth", Proc. 24th International Colloquium on Automata, Languages and Programming (ICALP '97), Lecture Notes in Computer Science, vol. 1256, Springer-Verlag, pp. 627–637, doi:10.1007/3-540-63165-8_217, hdl:2117/96447, ISBN 978-3-540-63165-1. Fomin, Fedor V.; Mazoit, Frédéric; Todinca, Ioan (2009), "Computing branchwidth via efficient triangulations and blocks", Discrete Applied Mathematics, 157 (12): 2726–2736, doi:10.1016/j.dam.2008.08.009.

icm2006.org

Geelen, Gerards & Whittle (2006). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842.
Geelen, Gerards & Whittle (2002); Geelen, Gerards & Whittle (2006). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2002), "Branch-width and well-quasi-ordering in matroids and graphs", Journal of Combinatorial Theory, Series B, 84 (2): 270–290, doi:10.1006/jctb.2001.2082. Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842.
Geelen, Gerards & Whittle (2006); Geelen, Gerards & Whittle (2007). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842. Geelen, Jim; Gerards, Bert; Whittle, Geoff (2007), "Excluding a planar graph from GF(q)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 97 (6): 971–998, doi:10.1016/j.jctb.2007.02.005, archived from the original (PDF) on 2010-09-24.

muni.cz

fi.muni.cz

Hliněný & Whittle (2006). Hliněný, Petr; Whittle, Geoff (2006), "Matroid tree-width" (PDF), European Journal of Combinatorics, 27 (7): 1117–1128, doi:10.1016/j.ejc.2006.06.005, archived from the original (PDF) on 2012-03-06, retrieved 2010-07-06.

rice.edu

caam.rice.edu

Hicks (2000); Hliněný (2003). Hicks, Illya V. (2000), Branch Decompositions and their Applications, Ph.D. thesis, Rice University, archived from the original on 2011-07-16, retrieved 2010-07-06. Hliněný, Petr (2003), "On matroid properties definable in the MSO logic", Proc. 28th International Symposium on Mathematical Foundations of Computer Science (MFCS '03), Lecture Notes in Computer Science, vol. 2747, Springer-Verlag, pp. 470–479, doi:10.1007/978-3-540-45138-9\_41 (inactive 1 November 2024){{citation}}: CS1 maint: DOI inactive as of November 2024 (link)

uwaterloo.ca

math.uwaterloo.ca

Geelen, Gerards & Whittle (2006); Geelen, Gerards & Whittle (2007). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842. Geelen, Jim; Gerards, Bert; Whittle, Geoff (2007), "Excluding a planar graph from GF(q)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 97 (6): 971–998, doi:10.1016/j.jctb.2007.02.005, archived from the original (PDF) on 2010-09-24.

web.archive.org

Hicks (2000); Hliněný (2003). Hicks, Illya V. (2000), Branch Decompositions and their Applications, Ph.D. thesis, Rice University, archived from the original on 2011-07-16, retrieved 2010-07-06. Hliněný, Petr (2003), "On matroid properties definable in the MSO logic", Proc. 28th International Symposium on Mathematical Foundations of Computer Science (MFCS '03), Lecture Notes in Computer Science, vol. 2747, Springer-Verlag, pp. 470–479, doi:10.1007/978-3-540-45138-9\_41 (inactive 1 November 2024){{citation}}: CS1 maint: DOI inactive as of November 2024 (link)
Hliněný & Whittle (2006). Hliněný, Petr; Whittle, Geoff (2006), "Matroid tree-width" (PDF), European Journal of Combinatorics, 27 (7): 1117–1128, doi:10.1016/j.ejc.2006.06.005, archived from the original (PDF) on 2012-03-06, retrieved 2010-07-06.
- Geelen, Gerards & Whittle (2006); Geelen, Gerards & Whittle (2007). Geelen, Jim; Gerards, Bert; Whittle, Geoff (2006), "Towards a structure theory for matrices and matroids" (PDF), Proc. International Congress of Mathematicians, vol. III, pp. 827–842. Geelen, Jim; Gerards, Bert; Whittle, Geoff (2007), "Excluding a planar graph from GF(q)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 97 (6): 971–998, doi:10.1016/j.jctb.2007.02.005, archived from the original (PDF) on 2010-09-24.