Cycles through prescribed vertices with large degree sum
نویسندگان
چکیده
منابع مشابه
Packing cycles through prescribed vertices
The well-known theorem of Erdős and Pósa says that a graph G has either k vertex-disjoint cycles or a vertex set X of order at most f(k) such that G\X is a forest. Starting with this result, there are many results concerning packing and covering cycles in graph theory and combinatorial optimization. In this paper, we generalize Erdős-Pósa’s result to cycles that are required to go through a set...
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Let k ≥ 2 and n ≥ 1 be integers, let G be a graph of order n with minimum degree at least k + 1. Let v1, v2, · · · , vk be k distinct vertices of G, and suppose that there exist k vertex disjoint cycles C1, · · · , Ck in G such that vi ∈ V (Ci) for each 1 ≤ i ≤ k. Suppose further that the minimum value of the sum of the degrees of two nonadjacent distinct vertices is greater than or equal to n ...
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We prove that for every graph, any vertex subset S, and given integers k, `: there are k disjoint cycles of length at least ` that each contain at least one vertex from S, or a vertex set of size O(` · k log k) that meets all such cycles. This generalises previous results of Fiorini and Hendrickx and of Pontecorvi and Wollan. In addition, we describe an algorithm for our main result that runs i...
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Guaranteed upper bounds on the length of a shortest cycle through k ≤ 5 prescribed vertices of a polyhedral graph or plane triangulation are proved.
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For c 2 and k minfc; 3g, guaranteed upper bounds on the length of a shortest cycle through k prescribed vertices of a c-connected graph are proved. Analogous results on planar graphs are presented, too.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00036-i