Colored graphs without colorful cycles
نویسندگان
چکیده
منابع مشابه
Colored graphs without colorful cycles
A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a colored graph lacks colorful cycles iff it is Gallai, i.e., lacks colorful triangles. We then show that, under the operation m◦n ≡ m+n−2, the omitted lengths of colorful cycles in a colored graph form a monoid isomorp...
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We study the following two functions: d(n, c) and ~ d(n, c); d(n, c) (~ d(n, c)) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and minimum monochromatic degree (out-degree) at least k has a properly colored cycle. Abouelaoualim et al. (2007) stated a conjecture which implies that d(n, c) = 1. Using a recursive construction of c-edge-colored graphs...
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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...
متن کاملProperly 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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ژورنال
عنوان ژورنال: Combinatorica
سال: 2007
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-007-2224-6