منابع مشابه
Grid Minors in Damaged Grids
We prove upper and lower bounds on the size of the largest square grid graph that is a subgraph, minor, or shallow minor of a graph in the form of a larger square grid from which a specified number of vertices have been deleted. Our bounds are tight to within constant factors. We also provide less-tight bounds on analogous problems for higher-dimensional grids.
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A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t ≥ 1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c = c(k) independent of G such that the complement of G has a minor isomorphic to Ks, where s = d2 (1 + 1/t)n − ce. We prove that Kostochka’s conjecture i...
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Introduction We examine issues involved in creating “virtual Grids” out of specific Grid installations. We see it as inevitable that Grids will be established as islands of resource collections that will need to be federated in lightweight manners. These islands of resources may result from a number of reasons. First, a group may set up a Grid of resources that it owns and directly controls but...
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For every integer t there is a smallest real number c(t) such that any graph with average degree at least c(t) must contain a Kt-minor (proved by Mader). Improving on results of Shapira and Sudakov, we prove the conjecture of Fiorini, Joret, Theis and Wood that any graph with n vertices and average degree at least c(t) + ε must contain a Kt-minor consisting of at most C(ε, t) logn vertices. Mad...
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s Elgersburg 2011 Rainbow Cycles in Cube Graphs Jens-P. Bode (Technische Universität Braunschweig) Joint work with A. Kemnitz and S. Struckmann A graph G is called rainbow with respect to an edge coloring if no two edges of G have the same color. Given a host graph H and a guest graph G ⊆ H, an edge coloring of H is called G-anti-Ramsey if no subgraph of H isomorphic to G is rainbow. The anti-R...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1989
ISSN: 0095-8956
DOI: 10.1016/0095-8956(89)90033-6