Alternating eulerian trails with prescribed degrees in two edge-colored complete graphs
نویسندگان
چکیده
منابع مشابه
Long Alternating Cycles in Edge-Colored Complete Graphs
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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∗Sponsored by French Ministry of Education †Sponsored by Conselho Nacional de Desenvolvimento Cient́ıfico e Tecnológico CNPq ‡Sponsored by Conselho Nacional de Desenvolvimento Cient́ıfico e Tecnológico CNPq
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In this paper we deal from an algorithmic perspective with different questions regarding properly edge-colored (or PEC) paths, trails and closed trails. Given a c-edge-colored graph G, we show how to polynomially determine, if any, a PEC closed trail subgraph whose number of visits at each vertex is specified before hand. As a consequence, we solve a number of interesting related problems. For ...
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Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we prove that an edgecolored multigraph of order n on at least three colors and with minimum colored degree greater than or equal to d 2 e has properly edge-colored cycles of all possible lengths, including hamiltonian c...
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In this paper we deal from an algorithmic perspective with different questions regarding monochromatic and properly edge-colored s-t paths/trails on edge-colored graphs. Given a c-edge-colored graph Gc without properly edge-colored closed trails, we present a polynomial time procedure for the determination of properly edgecolored s-t trails visiting all vertices of Gc a prescribed number of tim...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1983
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90016-x