Rainbow Matchings in Properly Colored Bipartite Graphs
نویسندگان
چکیده
منابع مشابه
Rainbow Matchings in Properly Colored Bipartite Graphs
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 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 کاملLarge Rainbow Matchings in Edge-Colored Graphs
A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident with v. Wang and Li conjectured that for k ≥ 4, every edge-colored graph with minimum color degree k contains a rainbow matching of size at least dk/2e. A properly edge-colored K4 has no such matching, which motivates the ...
متن کاملOn rainbow matchings in bipartite graphs
We present recent results regarding rainbow matchings in bipartite graphs. Using topological methods we address a known conjecture of Stein and show that if Kn,n is partitioned into n sets of size n, then a partial rainbow matching of size 2n/3 exists. We generalize a result of Cameron and Wanless and show that for any n matchings of size n in a bipartite graph with 2n vertices there exists a f...
متن کاملRainbow Matchings of Size δ(G) in Properly Edge-Colored Graphs
A rainbow matching in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(δ) such that a properly edgecolored graph G with minimum degree δ and order at least f(δ) must have a rainbow matching of size δ. We answer this question in the affirmative; an extremal approach yields that f(δ) = 98δ/23 < 4.27δ suffices. Furthermore, we giv...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2012
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2012.22011