منابع مشابه
Linkages in Polytope Graphs
A graph is k-linked if any k disjoint vertex-pairs can be joined by k disjoint paths. We improve a lower bound on the linkedness of polytopes slightly, which results in exact values for the minimal linkedness of 7-, 10and 13-dimensional polytopes. We analyze in detail linkedness of polytopes on at most (6d + 7)/5 vertices. In that case, a sharp lower bound on minimal linkedness is derived, and ...
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We show that deciding whether a graph with given edge lengths can be realized by a straight-line drawing has the same complexity as deciding the truth of sentences in the existential theory of the real numbers, ETR; we introduce the class ∃R that captures the computational complexity of ETR and many other problems. The graph realizability problem remains ∃R-complete if all edges have unit lengt...
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The Disjoint-Paths Problem asks, given a graph G and a set of pairs of terminals (s1, t1), . . . , (sk, tk), whether there is a collection of k pairwise vertex-disjoint paths linking si and ti, for i = 1, . . . , k. In their f(k) · n algorithm for this problem, Robertson and Seymour introduced the irrelevant vertex technique according to which in every instance of treewidth greater than g(k) th...
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In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been made and we hope to the contrary that this thesis contains some important advances and that the reader will share this point of view. Unders...
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In this paper we consider a well-known class of valid inequalities for the p-median and the uncapacitated facility location polytopes, the odd cycle inequalities. It is known that their separation problem is polynomially solvable. We give a new polynomial separation algorithm based on a reduction from the original graph. Then, we define a non-trivial class of graphs, where the odd cycle inequal...
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ژورنال
عنوان ژورنال: advg
سال: 2011
ISSN: 1615-7168,1615-715X
DOI: 10.1515/advgeom.2011.015