Properly colored paths and cycles
نویسندگان
چکیده
منابع مشابه
Canonical Ramsey numbers and properly colored cycles
We improve the previous bounds on the so-called unordered Canonical Ramsey numbers, introduced by Richer [D. Richer, Unordered canonical Ramsey numbers, Journal of Combinatorial Theory Series B 80 (2000) 172–177] as a variant of the canonical Ramsey numbers introduced by Erdős and Rado [P. Erdős, R. Rado, A combinatorial theorem, Journal of the London Mathematical Society 25 (4) (1950) 249–255]...
متن کاملProperly colored trails, paths, and bridges
The proper-trail connection number of a graph is the minimum number of colors needed to color the edges such that every pair of vertices are joined by a trail without two consecutive edges of the same color; the proper-path connection number is defined similarly. In this paper we consider these in both bridgeless graphs and graphs in general. The main result is that both parameters are tied to ...
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 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 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.
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: Discrete Applied Mathematics
سال: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.06.005