Results 11 to 20 of about 39,621 (255)
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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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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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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The probability of planarity of a random graph near the critical point [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Erdős and Rényi conjectured in 1960 that the limiting probability $p$ that a random graph with $n$ vertices and $M=n/2$ edges is planar exists. It has been shown that indeed p exists and is a constant strictly between 0 and 1.
Marc Noy +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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Complete graph minors and the graph minor structure theorem
Journal of Combinatorial Theory, Series B, 2013 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 width, a bounded number of apex vertices, and the clique-sum operation.
Gwenaël Joret, David R. Wood
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Stem Cell Research & Therapy, 2021 Background We explored whether stem cell therapy was effective for animal models and patients with Crohn’s disease (CD). Methods We searched five online databases. The relative outcomes were analyzed with the aid of GetData Graph Digitizer 2.26 and Stata
Ruo Wang +7 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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