Properly colored Hamilton cycles in edge-colored complete graphs
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.
متن کاملLong properly colored cycles in edge colored complete graphs
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...
متن کاملOn Edge-Colored Graphs Covered by Properly Colored Cycles
We characterize edge-colored graphs in which every edge belongs to some properly colored cycle. We obtain our result by applying a characterization of 1-extendable graphs.
متن کاملCharacterization of edge-colored complete graphs with properly colored Hamilton paths
An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C0 and a (possibly empty) collection of properly colored cycles C1, C2, . . . , Cd such that V (Ci) ...
متن کاملRainbow Matchings in Properly Edge Colored Graphs
Let G be a properly edge colored graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree of G. We show that if |V (G)| ≥ 8δ 5 , then G has a rainbow matching of size at least ⌊ 5 ⌋. We also prove that if G is a properly colored triangle-free graph, then G has a rainbow matching of size at least ⌊ 3 ⌋.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures and Algorithms
سال: 1997
ISSN: 1042-9832,1098-2418
DOI: 10.1002/(sici)1098-2418(199709)11:2<179::aid-rsa5>3.0.co;2-p