Edge coloring of hypergraphs and a conjecture of ErdÖs, Faber, Lovász

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].

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References

  1. [1]

    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.

  2. [2]

    P. Erdős, On the combinatorial problems which I would most like to see solved,Combinatorica 1 (1981), 25–42.

    Google Scholar 

  3. [3]

    P.Erdős, Selected problems,in: Progress in Graph Theory (J. A. Bondy and U. S. R. Murty, eds.), Academic Press, (1984), 528–531.

  4. [4]

    N. Hindman, On a conjecture of Erdős, Faber and Lovász aboutn-colorings,Canadian J. Math. 33 (1981), 563–570.

    Google Scholar 

  5. [5]

    P. D. Seymour, Packing nearly-disjoint sets,Combinatorica 2 (1982), 91–97.

    Google Scholar 

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This research was partially supported by N.S.F. grant No. MCS-8311422.

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Chang, W.I., Lawler, E.L. Edge coloring of hypergraphs and a conjecture of ErdÖs, Faber, Lovász. Combinatorica 8, 293–295 (1988). https://doi.org/10.1007/BF02126801

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AMS subject classification (1980)

  • 05 C 15
  • 05 C 65