On a Generalization of the Ryser-Brualdi-Stein Conjecture
نویسندگان
چکیده
A rainbow matching for (not necessarily distinct) sets F1, . . . , Fk of hypergraph edges is a matching consisting of k edges, one from each Fi. The aim of the paper is twofold to put order in the multitude of conjectures that relate to this concept (some of them first presented here), and to present some partial results on one of these conjectures, that seems central among them.
منابع مشابه
Rainbow matchings and connectedness of coloured graphs
Aharoni and Berger conjectured that every bipartite graph which is the union of n matchings of size n + 1 contains a rainbow matching of size n. This conjecture is a generalization of several old conjectures of Ryser, Brualdi, and Stein about transversals in Latin squares. When the matchings are all edge-disjoint and perfect, an approximate version of this conjecture follows from a theorem of H...
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Aharoni and Berger conjectured that every collection of n matchings of size n+1 in a bipartite graph contains a rainbow matching of size n. This conjecture is related to several old conjectures of Ryser, Brualdi, and Stein about transversals in Latin squares. There have been many recent partial results about the Aharoni-Berger Conjecture. The conjecture is known to hold when the matchings are m...
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Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which ...
متن کاملAbstract—alexey Pokrovskiy
Alexey Pokrovskiy Aharoni and Berger conjectured [1] that every bipartite graph which is the union of n matchings of size n + 1 contains a rainbow matching of size n. This conjecture is related to several old conjectures of Ryser, Brualdi, and Stein about transversals in Latin squares. There have been many recent partial results about the Aharoni-Berger Conjecture. When the matchings have size ...
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عنوان ژورنال:
- Journal of Graph Theory
دوره 78 شماره
صفحات -
تاریخ انتشار 2015