Results 11 to 20 of about 168,763 (311)
Fast separation in a graph with an excluded minor [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $G$ be an $n$-vertex $m$-edge graph with weighted vertices. A pair of vertex sets $A,B \subseteq V(G)$ is a $\frac{2}{3} - \textit{separation}$ of $\textit{order}$ $|A \cap B|$ if $A \cup B = V(G)$, there is no edge between $A \backslash B$ and $B ...
Bruce Reed, David R. Wood
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MINORS IN WEIGHTED GRAPHS [PDF]
Bulletin of the Australian Mathematical Society, 2008 AbstractWe define the notion of minor for weighted graphs. We prove that with this minor relation, the set of weighted graphs is directed. We also prove that, given any two weights on a connected graph with the same total weight, we can transform one into the other using a sequence of edge subdivisions and edge contractions.
Joiţa, Cezar, Joiţa, Daniela
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Small minors in dense graphs [PDF]
European Journal of Combinatorics, 2012 A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of the whole graph.
Samuel Fiorini +3 more
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Modularity of minor‐free graphs
Journal of Graph Theory, 2022 AbstractWe prove that a class of graphs with excluded minor and with the maximum degree of smaller order than the number of edges is maximally modular, that is, for every , the modularity of any graph in the class with sufficiently many edges is at least .
Michal Lason, Malgorzata Sulkowska
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, 2019 In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph where k ≥ 2. If G contains three k-cliques, say L 1, L2, L3, such that |Li ∩ Lj| ≤ k - 2 (1 ≤ i \u3c j ≤ 3), then G contains a Kk +2 as a minor.
Niu, Jianbing
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The Minor Crossing Number of Graphs with an Excluded Minor [PDF]
The Electronic Journal of Combinatorics, 2008 The minor crossing number of a graph $G$ is the minimum crossing number of a graph that contains $G$ as a minor. It is proved that for every graph $H$ there is a constant $c$, such that every graph $G$ with no $H$-minor has minor crossing number at most $c|V(G)|$.
Bokal, Drago +2 more
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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).
Benjamin R. Moore +2 more
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Upper Bounds on the Graph Minor Theorem [PDF]
, 2020 Lower bounds on the proof-theoretic strength of the graph minor theorem were found over 30 years ago by Friedman, Robertson and Seymour (Metamathematics of the graph minor theorem, pp 229–261, [4]), but upper bounds have always been elusive.
Rathjen, M +9 more
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Theoretical Computer Science, 2011 Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority rule.
Rouquier, Jean-Baptiste +2 more
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Testing first-order properties for subclasses of sparse graphs [PDF]
, 2013 We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nešetřil and Ossona de Mendez.
Thomas, Robin +2 more
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