Approximability of Packing Disjoint Cycles
نویسندگان
چکیده
منابع مشابه
Disjoint Even Cycles Packing
We generalize the well-known theorem of Corrádi and Hajnal which says that if a given graph G has at least 3k vertices and the minimum degree of G is at least 2k, then G contains k vertex-disjoint cycles. Our main result is the following; for any integer k, there is an absolute constant ck satisfying the following; let G be a graph with at least ck vertices such that the minimum degree of G is ...
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For a graph G, let ν(G) and ν ′(G) denote the maximum cardinalities of packings of vertex-disjoint and edge-disjoint cycles of G, respectively. We study the interplay of these two parameters and vertex cuts in graphs. If G is a graph whose vertex set can be partitioned into three non-empty sets S, V1, and V2 such that there is no edge between V1 and V2, and k = |S|, then our results imply that ...
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For a graph G let μ(G) denote the cyclomatic number and let ν(G) denote the maximum number of edge-disjoint cycles of G. We prove that for every k ≥ 0 there is a finite set P(k) such that every 2-connected graph G for which μ(G)− ν(G) = k arises by applying a simple extension rule to a graph in P(k). Furthermore, we determine P(k) for k ≤ 2 exactly.
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We give an fpt approximation algorithm for the directed vertex disjoint cycle problem. Given a directed graph G with n vertices and a positive integer k, the algorithm constructs a family of at least k/ρ(k) disjoint cycles of G if the graph G has a family of at least k disjoint cycles (and otherwise may still produce a solution, or just report failure). Here ρ is a computable function such that...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2009
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-009-9349-5