Exchange systems, matchings, and transversals
نویسندگان
چکیده
منابع مشابه
Rainbow matchings and transversals
We show that there exists a bipartite graph containing n matchings of sizes mi n satisfying ∑ i mi = n 2 + n/2 − 1, such that the matchings have no rainbow matching. This answers a question posed by Aharoni, Charbit and Howard. We also exhibit (n − 1) × n latin rectangles that cannot be decomposed into transversals, and some related constructions. In the process we answer a question posed by Hä...
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In this paper we consider properly edge-colored graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A matching is called rainbow if its edges have different colors. The minimum degree of a graph is denoted by δ(G). We show that properly edge colored graphs G with |V (G)| ≥ 4δ(G) − 3 have rainbow matchings of size δ(G), this gives the best know...
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In this paper we show that properly edge-colored graphs Gwith |V (G)| ≥ 4δ(G) − 3 have rainbow matchings of size δ(G); this gives the best known bound for a recent question of Wang. We also show that properly edge-colored graphs Gwith |V (G)| ≥ 2δ(G) have rainbow matchings of size at least δ(G) − 2δ(G)2/3. This result extends (with a weaker error term) the well-known result that a factorization...
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We state and prove a theorem (Theorem 1 below) which strengthens previously known results concerning disjoint common partial transversals of two families of sets. This theorem may be viewed as a result on transversal pre-independence structures. We define a "disjoint-exchange structure" on a set and extend the result to such structures (Theorem 3 below). Then we give an application of this theo...
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Given a system (V, f, d) on a finite set V consisting of two set functions f : 2 → R and d : 2 → R, we consider the problem of finding a set R ⊆ V of minimum cardinality such that f(X) ≥ d(X) for all X ⊆ V − R, where the problem can be regarded as a natural generalization of the source location problems and the external network problems in (undirected) graphs and hypergraphs. We give a structur...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1968
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(68)80071-7