Relevant bibliographies by topics / Excluded-minor theorem

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Excluded-minor theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Excluded-minor theorem"

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Thomas, Robin. "A counter-example to ‘Wagner's conjecture’ for infinite graphs." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 1 (1988): 55–57. http://dx.doi.org/10.1017/s0305004100064616.

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Wagner made the conjecture that given an infinite sequence G1, G2, … of finite graphs there are indices i < j such that Gi is a minor of Gj. (A graph is a minor of another if the first can be obtained by contraction from a subgraph of the second.) The importance of this conjecture is that it yields excluded minor theorems in graph theory, where by an excluded minor theorem we mean a result asserting that a graph possesses a specified property if and only if none of its minors belongs to a finite list of ‘forbidden minors’. A widely known example of an excluded minor theorem is Kuratowski's
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Maharry, John. "An excluded minor theorem for the octahedron." Journal of Graph Theory 31, no. 2 (1999): 95–100. http://dx.doi.org/10.1002/(sici)1097-0118(199906)31:2<95::aid-jgt2>3.0.co;2-n.

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Mohar, Bojan. "The excluded minor structure theorem with planarly embedded wall." Ars Mathematica Contemporanea 6, no. 2 (2012): 187–96. http://dx.doi.org/10.26493/1855-3974.118.3dd.

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Maharry, John. "An excluded minor theorem for the Octahedron plus an edge." Journal of Graph Theory 57, no. 2 (2007): 124–30. http://dx.doi.org/10.1002/jgt.20272.

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Thomassen, Carsten. "A Simpler Proof of the Excluded Minor Theorem for Higher Surfaces." Journal of Combinatorial Theory, Series B 70, no. 2 (1997): 306–11. http://dx.doi.org/10.1006/jctb.1997.1761.

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Diestel, Reinhard, Ken-ichi Kawarabayashi, Theodor Müller, and Paul Wollan. "On the excluded minor structure theorem for graphs of large tree-width." Journal of Combinatorial Theory, Series B 102, no. 6 (2012): 1189–210. http://dx.doi.org/10.1016/j.jctb.2012.07.001.

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FIORINI, SAMUEL, GWENAËL JORET, and DAVID R. WOOD. "Excluded Forest Minors and the Erdős–Pósa Property." Combinatorics, Probability and Computing 22, no. 5 (2013): 700–721. http://dx.doi.org/10.1017/s0963548313000266.

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A classical result of Robertson and Seymour states that the set of graphs containing a fixed planar graph H as a minor has the so-called Erdős–Pósa property; namely, there exists a function f depending only on H such that, for every graph G and every positive integer k, the graph G has k vertex-disjoint subgraphs each containing H as a minor, or there exists a subset X of vertices of G with |X| ≤ f(k) such that G − X has no H-minor (see Robertson and Seymour, J. Combin. Theory Ser. B41 (1986) 92–114). While the best function f currently known is exponential in k, a O(k log k) bound is known in
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Gubser, Bradley S. "A Characterization of Almost-Planar Graphs." Combinatorics, Probability and Computing 5, no. 3 (1996): 227–45. http://dx.doi.org/10.1017/s0963548300002005.

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Kuratowski's Theorem, perhaps the most famous result in graph theory, states that K5 and K3,3 are the only non-planar graphs for which both G\e, the deletion of the edge e, and G/e, the contraction of the edge e, are planar for all edges e of G. We characterize the almost-planar graphs, those non-planar graphs for which G\e or G/e is planar for all edges e of G. This paper gives two characterizations of the almost-planar graphs: an explicit description of the structure of almost-planar graphs; and an excluded minor criterion. We also give a best possible bound on the number of edges of an almo
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Oxley, James, and Geoff Whittle. "Some excluded-minor theorems for a class of polymatroids." Combinatorica 13, no. 4 (1993): 467–76. http://dx.doi.org/10.1007/bf01303518.

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Andreae, Thomas. "On a pursuit game played on graphs for which a minor is excluded." Journal of Combinatorial Theory, Series B 41, no. 1 (1986): 37–47. http://dx.doi.org/10.1016/0095-8956(86)90026-2.

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Dissertations / Theses on the topic "Excluded-minor theorem"

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Zhou, Xiangqian. "Some Excluded-Minor Theorems for Binary Matroids." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1070311692.

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Müller, Theodor [Verfasser], and Reinhard [Akademischer Betreuer] Diestel. "The excluded minor structure theorem, and linkages in large graphs of bounded tree-width / Theodor Müller. Betreuer: Reinhard Diestel." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://d-nb.info/1050239148/34.

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Müller, Theodor Verfasser], and Reinhard [Akademischer Betreuer] [Diestel. "The excluded minor structure theorem, and linkages in large graphs of bounded tree-width / Theodor Müller. Betreuer: Reinhard Diestel." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://nbn-resolving.de/urn:nbn:de:gbv:18-67087.

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Book chapters on the topic "Excluded-minor theorem"

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Oxley, James. "Excluded-Minor Theorems." In Matroid Theory. Oxford University Press, 2011. http://dx.doi.org/10.1093/acprof:oso/9780198566946.003.0011.

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Thomas, Robin. "Recent Excluded Minor Theorems for Graphs." In Surveys in Combinatorics, 1999. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511721335.008.

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Conference papers on the topic "Excluded-minor theorem"

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Alon, N., P. Seymour, and R. Thomas. "A separator theorem for graphs with an excluded minor and its applications." In the twenty-second annual ACM symposium. ACM Press, 1990. http://dx.doi.org/10.1145/100216.100254.

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