Edge coloring of hypergraphs and a conjecture of ErdÖs, Faber, Lovász
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Call a bypergraphsimple if for any pairu, v of distinct vertices, there is at most one edge incident to bothu andv, and there are no edges incident to exactly one vertex. A conjecture of Erdős, Faber and Lovász is equivalent to the statement that the edges of any simple hypergraph onn vertices can be colored with at mostn colors. We present a simple proof that the edges of a simple hypergraph onn vertices can be colored with at most [1.5n-2 colors].
AMS subject classification (1980)05 C 15 05 C 65
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- P.Erdős, Problems and results in graph theory and combinatorial analysis,in: Graph Theory and Related Topics (J. A. Bondy and U. S. R. Murty, eds.), Academic Press, (1978), 153–163.Google Scholar
- P. Erdős, On the combinatorial problems which I would most like to see solved,Combinatorica 1 (1981), 25–42.Google Scholar
- P.Erdős, Selected problems,in: Progress in Graph Theory (J. A. Bondy and U. S. R. Murty, eds.), Academic Press, (1984), 528–531.Google Scholar
- N. Hindman, On a conjecture of Erdős, Faber and Lovász aboutn-colorings,Canadian J. Math. 33 (1981), 563–570.Google Scholar
- P. D. Seymour, Packing nearly-disjoint sets,Combinatorica 2 (1982), 91–97.Google Scholar