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Graph minors. XXI. Graphs with unique linkages

Journal of Combinatorial Theory Series B, 2009
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Paul Seymour
exaly   +4 more sources

Graph Minors and Metric Spaces

Combinatorica, 2023
We present problems and results that combine graph-minors and coarse geometry. For example, we ask whether every geodesic metric space (or graph) without a fat H minor is quasi-isometric to a graph with no H minor, for an arbitrary finite graph H.
Agelos Georgakopoulos, P. Papasoglu
semanticscholar   +6 more sources

Complete graph minors and the graph minor structure theorem [PDF]

Journal of Combinatorial Theory, Series B, 2011
The graph minor structure theorem by Robertson and Seymour shows that every graph that excludes a fixed minor can be constructed by a combination of four ingredients: graphs embedded in a surface of bounded genus, a bounded number of vortices of bounded ...
G. Joret, D. Wood
semanticscholar   +4 more sources

Reconfiguration of graph minors

CoRR, 2018
Under the reconfiguration framework, we consider the various ways that a target graph $H$ is a {\em minor} of a host graph $G$, where a subgraph of $G$ can be transformed into $H$ by means of {\em edge contraction} (replacement of both endpoints of an edge by a new vertex adjacent to any vertex adjacent to either endpoint).
B. Moore, N. Nishimura, V. Subramanya
semanticscholar   +5 more sources

On the extremal function for graph minors [PDF]

Journal of Graph Theory, 2019
For a graph H $H$ , let c(H)=inf{c:e(G)≥c|G|impliesG≻H} $c(H)=\text{inf}\{c:e(G)\ge c|G|\,\,\text{implies}\,\,G\succ H\}$ , where G≻H $G\succ H$ means that H $H$ is a minor of G $G$ .
A. Thomason, Matthew Wales
semanticscholar   +5 more sources

Graph Minors: XV. Giant Steps

Journal of Combinatorial Theory, Series B, 1996
The main result of this series serves to reduce several problems about general graphs to problems about graphs which can “almost” be drawn in surfaces of bounded genus. In applications of the theorem we usually need to encode such a nearly embedded graph as a hypergraph which can be drawn completely in the surface.
N. Robertson, P. Seymour
semanticscholar   +2 more sources

Graph minors. V. Excluding a planar graph

Journal of Combinatorial Theory, Series B, 1986
[For part I see the authors' paper ibid. 35, 39-61 (1983; Zbl 0521.05062), for part III see their paper ibid. 36, 49-64 (1984; Zbl 0548.05025), for part VI see ibid., 115-138 (1986; Zbl 0598.05042). See also their survey paper in Surveys in Combinatorics 1985, Pap. 10th Br. Combin. Conf., Glasgow/Scotl. 1985, Lond. Math. Soc. Lect. Note Ser.
N. Robertson, P. Seymour
semanticscholar   +2 more sources

Explicit bounds for graph minors [PDF]

Journal of Combinatorial Theory, Series B, 2013
Let $\Sigma$ be a surface with boundary $b(\Sigma)$, $\mathcal{L}$ be a collection of $k$ disjoint $b(\Sigma)$-paths in $\Sigma$, and $P$ be a non-separating $b(\Sigma)$-path in $\Sigma$.
J. Geelen, T. Huynh, R. Richter
semanticscholar   +7 more sources

Graph minors XXIII. Nash-Williams' immersion conjecture

Journal of Combinatorial Theory Series B, 2010
Paul Seymour
exaly   +2 more sources

Graph Minors .XIII. The Disjoint Paths Problem

Journal of Combinatorial Theory Series B, 1995
N. Robertson, P. Seymour
exaly   +2 more sources