Random Graphs with Few Disjoint Cycles
نویسندگان
چکیده
منابع مشابه
Random Graphs with Few Disjoint Cycles
The classical Erdős-Pósa theorem states that for each positive integer k there is an f(k) such that, in each graph G which does not have k + 1 disjoint cycles, there is a blocker of size at most f(k); that is, a set B of at most f(k) vertices such that G − B has no cycles. We show that, amongst all such graphs on vertex set {1, . . . , n}, all but an exponentially small proportion have a blocke...
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The Erdős-Pósa theorem (1965) states that in each graph G which contains at most k disjoint cycles, there is a ‘blocking’ set B of at most f(k) vertices such that the graph G − B is acyclic. Robertson and Seymour (1986) give an extension concerning any minor-closed class A of graphs, as long as A does not contain all planar graphs: in each graph G which contains at most k disjoint excluded mino...
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Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2011
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548311000186