Abstract
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].
Similar content being viewed by others
References
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.
P. Erdős, On the combinatorial problems which I would most like to see solved,Combinatorica 1 (1981), 25–42.
P.Erdős, Selected problems,in: Progress in Graph Theory (J. A. Bondy and U. S. R. Murty, eds.), Academic Press, (1984), 528–531.
N. Hindman, On a conjecture of Erdős, Faber and Lovász aboutn-colorings,Canadian J. Math. 33 (1981), 563–570.
P. D. Seymour, Packing nearly-disjoint sets,Combinatorica 2 (1982), 91–97.
Author information
Authors and Affiliations
Additional information
This research was partially supported by N.S.F. grant No. MCS-8311422.