Rainbow Matchings in Properly-Colored Hypergraphs
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 کاملRainbow matchings in properly-coloured multigraphs
Aharoni and Berger conjectured that in any bipartite multigraph that is properly edge-coloured by n colours with at least n + 1 edges of each colour there must be a matching that uses each colour exactly once. In this paper we consider the same question without the bipartiteness assumption. We show that in any multigraph with edge multiplicities o(n) that is properly edge-coloured by n colours ...
متن کاملOn rainbow matchings for hypergraphs
For any posotive integer m, let [m] := {1, . . . ,m}. Let n, k, t be positive integers. Aharoni and Howard conjectured that if, for i ∈ [t], Fi ⊂ [n] := {(a1, . . . , ak) : aj ∈ [n] for j ∈ [k]} and |Fi| > (t−1)n, then there exist M ⊆ [n] such that |M | = t and |M ∩ Fi| = 1 for i ∈ [t] We show that this conjecture holds when n ≥ 3(k − 1)(t− 1). Let n, t, k1 ≥ k2 ≥ . . . ≥ kt be positive integer...
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: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8125