Coloring Graphs to Produce Properly Colored Walks
نویسندگان
چکیده
منابع مشابه
Coloring Graphs to Produce Properly Colored Walks
For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair of vertices without two consecutive edges having the same color. We show that the proper-walk connection number is at most three for all cyclic graphs, and at most two for bridgeless graphs. We also characterize the bi...
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Let G be a properly colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition ( X , Y ) and . We show that if = G k 3 7 max , 4 k X Y , then G has a rainbow coloring of size at least 3 4 k .
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 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 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...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2017
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-017-1843-y