Hamiltonian problems in edge-colored complete graphs and eulerian cycles in edge-colored graphs : some complexity results
نویسندگان
چکیده
منابع مشابه
Properly colored Hamilton cycles in edge-colored complete graphs
It is shown that for every > 0 and n > n0( ), any complete graph K on n vertices whose edges are colored so that no vertex is incident with more than (1 − 1 √ 2 − )n edges of the same color, contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and n any such K contains a cycle of length k in which adjacent edges have distinct colors.
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Let Kc n denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(Kc n) denote the maximum number of edges of the same color incident with a vertex of Kn. A properly colored cycle (path) in Kc n is a cycle (path) in which adjacent edges have distinct colors. B. Bollobás and P. Erdös (1976) proposed the following conjecture: If ∆mon(Kc n) < b 2 c, then Kc n con...
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We first consider the following problem. We are given a fixed perfect matching M of [n] and we add random edges one at a time until there is a Hamilton cycle containing M . We show that w.h.p. the hitting time for this event is the same as that for the first time there are no isolated vertices in the graph induced by the random edges. We then use this result for the following problem. We genera...
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Let K n denote a complete graph on n vertices whose edges are colored in an arbitrary way. And let ∆(K n) denote the maximum number of edges of the same color incident with a vertex of K n. A properly colored cycle (path) in K n, that is, a cycle (path) in which adjacent edges have distinct colors is called an alternating cycle (path). Our note is inspired by the following conjecture by B. boll...
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Let G be a graph of order n with an edge coloring c, and let δ(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least δ(G) edges having pairwise distinct colors. A subgraph F ⊂ G is rainbow if all edges of F have pairwise distinct colors. In this paper, we prove that (i) if G is triangle-free and δ(G) > n3 + 1, then G contains a r...
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ژورنال
عنوان ژورنال: RAIRO - Operations Research
سال: 1996
ISSN: 0399-0559,1290-3868
DOI: 10.1051/ro/1996300404171