Results 11 to 20 of about 1,862,441 (301)
Graph Minors. XXII. Irrelevant vertices in linkage problems
Journal of Combinatorial Theory Series B, 2012 In the algorithm for the disjoint paths problem given in Graph Minors XIII, we used without proof a lemma that, in solving such a problem, a vertex which was sufficiently “insulated” from the rest of the graph by a large planar piece of the graph was ...
Paul Seymour
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Graph minors. X. Obstructions to tree-decomposition
Journal of Combinatorial Theory Series B, 1991 Roughly, a graph has small “tree-width” if it can be constructed by piecing small graphs together in a tree structure. Here we study the obstructions to the existence of such a tree structure.
N. Robertson, P. Seymour
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Optimizing the Graph Minors Weak Structure Theorem [PDF]
SIAM Journal on Discrete Mathematics, 2011 One of the major results of [N. Robertson and P. D. Seymour, Graph minors. XIII. The disjoint paths problem, J. Combin. Theory Ser. B, 63 (1995), pp. 65--110], also known as the weak structure theorem, reveals the local structure of graphs excluding some
Archontia C. Giannopoulou, D. Thilikos
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The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations
AlgorithmsTree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width
Frank Gurski, Robin Weishaupt
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On cut polytopes and graph minors [PDF]
Discrete Optimization, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konstantinos Kaparis +2 more
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Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B, 2004 N. Robertson, P. Seymour
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Shallow Minors, Graph Products, and Beyond-Planar Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2021 The planar graph product structure theorem of Dujmovi\'{c}, Joret, Micek, Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path.
Robert Hickingbotham, D. Wood
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Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian.
Miriam Farber, Yelena Mandelshtam
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The sandpile group of a thick cycle graph
Electronic Journal of Graph Theory and Applications, 2022 The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.
Diane Christine Alar +4 more
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Minor-Universal Graph for Graphs on Surfaces
CoRR, 2023 We show that, for every n and every surface $Σ$, there is a graph U embeddable on $Σ$ with at most cn^2 vertices that contains as minor every graph embeddable on $Σ$ with n vertices. The constant c depends polynomially on the Euler genus of $Σ$. This generalizes a well-known result for planar graphs due to Robertson, Seymour, and Thomas [Quickly ...
Cyril Gavoille, Claire Hilaire
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