Loading...
Please wait, while we are loading the content...
Similar Documents
C O ] 2 4 M ay 2 01 8 Rainbow fractional matchings
| Content Provider | Semantic Scholar |
|---|---|
| Author | Aharoni, Ron Holzman, Ron Jiang, Zilin |
| Copyright Year | 2018 |
| Abstract | We prove that any family E1, . . . , E⌈rn⌉ of (not necessarily distinct) sets of edges in an r-uniform hypergraph, each having a fractional matching of size n, has a rainbow fractional matching of size n (that is, a set of edges from distinct Ei’s which supports such a fractional matching). When the hypergraph is r-partite and n is an integer, the number of sets needed goes down from rn to rn − r + 1. The problem solved here is a fractional version of the corresponding problem about rainbow matchings, which was solved by Drisko and by Aharoni and Berger in the case of bipartite graphs, but is open for general graphs as well as for r-partite hypergraphs with r > 2. Our topological proof is based on a result of Kalai and Meshulam about a simplicial complex and a matroid on the same vertex-set. MSC: 05D15; 55U10 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1805.09732 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
