# Fractional Aspects of the Erdős-Faber-Lovász Conjecture

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 1, page 197-202
- ISSN: 2083-5892

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topJohn Bosica, and Claude Tardif. "Fractional Aspects of the Erdős-Faber-Lovász Conjecture." Discussiones Mathematicae Graph Theory 35.1 (2015): 197-202. <http://eudml.org/doc/271234>.

@article{JohnBosica2015,

abstract = {The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lovász conjecture, involving variations of the fractional chromatic number. We exhibit some relaxations that can be proved in the spirit of the Kahn-Seymour result, and others that are equivalent to the original conjecture.},

author = {John Bosica, Claude Tardif},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Erdős-Faber-Lovász Conjecture; fractional chromatic number; Erdős-Faber-Lovász conjecture},

language = {eng},

number = {1},

pages = {197-202},

title = {Fractional Aspects of the Erdős-Faber-Lovász Conjecture},

url = {http://eudml.org/doc/271234},

volume = {35},

year = {2015},

}

TY - JOUR

AU - John Bosica

AU - Claude Tardif

TI - Fractional Aspects of the Erdős-Faber-Lovász Conjecture

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 1

SP - 197

EP - 202

AB - The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lovász conjecture, involving variations of the fractional chromatic number. We exhibit some relaxations that can be proved in the spirit of the Kahn-Seymour result, and others that are equivalent to the original conjecture.

LA - eng

KW - Erdős-Faber-Lovász Conjecture; fractional chromatic number; Erdős-Faber-Lovász conjecture

UR - http://eudml.org/doc/271234

ER -

## References

top- [1] N.G. de Bruijn and P. Erdős, On a combinatorial problem, Nederl. Akad. Wetensch. Zbl0032.24405
- Indag. Math 10 (1948) 421-423.
- [2] P. Erdős, R.C. Mullin, V.T. Sos and D.R. Stinson, Finite linear spaces and projective planes, Discrete Math. 47 (1983) 49-62. doi:10.1016/0012-365X(83)90071-7[Crossref] Zbl0521.51005
- [3] J. Kahn, Coloring nearly-disjoint hypergraphs with n+o(n) colors, J. Combin. The- ory (A) 59 (1992) 31-39. doi:10.1016/0097-3165(92)90096-D[Crossref]
- [4] J. Kahn and P.D. Seymour, A fractional version of the Erdős-Faber-Lovász conjec- ture, Combinatorica 12 (1992) 155-160. doi:10.1007/BF01204719[Crossref]
- [5] E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory (Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, New York, 1997).

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