# A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 3, page 545-549
- ISSN: 2083-5892

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topLucien Haddad, and Claude Tardif. "A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture." Discussiones Mathematicae Graph Theory 24.3 (2004): 545-549. <http://eudml.org/doc/270226>.

@article{LucienHaddad2004,

abstract = {The Erdős-Faber-Lovász conjecture states that if a graph G is the union of n cliques of size n no two of which share more than one vertex, then χ(G) = n. We provide a formulation of this conjecture in terms of maximal partial clones of partial operations on a set.},

author = {Lucien Haddad, Claude Tardif},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {chromatic number; Erdős-Faber-Lovász conjecture; maximal partial clones; partial operations},

language = {eng},

number = {3},

pages = {545-549},

title = {A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture},

url = {http://eudml.org/doc/270226},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Lucien Haddad

AU - Claude Tardif

TI - A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 3

SP - 545

EP - 549

AB - The Erdős-Faber-Lovász conjecture states that if a graph G is the union of n cliques of size n no two of which share more than one vertex, then χ(G) = n. We provide a formulation of this conjecture in terms of maximal partial clones of partial operations on a set.

LA - eng

KW - chromatic number; Erdős-Faber-Lovász conjecture; maximal partial clones; partial operations

UR - http://eudml.org/doc/270226

ER -

## References

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- [2] L. Haddad, Le treillis des clones partiels sur un univers fini et ses coatomes (Ph, D. thesis, Université de Montréal, 1986).
- [3] L. Haddad and I.G. Rosenberg, Critère général de complétude pour les algèbres partielles finies, C.R. Acad. Sci. Paris, tome 304, Série I, 17 (1987) 507-509. Zbl0617.08008
- [4] L. Haddad, Maximal partial clones determined by quasi-diagonal relations, J. Inf. Process. Cybern. EIK 24 (1988) 7/8 355-366. Zbl0665.08004
- [5] L. Haddad and I.G. Rosenberg, Maximal partial clones determined by areflexive relations, Discrete Appl. Math. 24 (1989) 133-143, doi: 10.1016/0166-218X(92)90279-J. Zbl0695.08010
- [6] L. Haddad, I.G. Rosenberg and D. Schweigert, A maximal partial clone and a S upecki-type criterion, Acta Sci. Math. 54 (1990) 89-98. Zbl0717.08003
- [7] L. Haddad and I.G. Rosenberg, Completeness theory for finite partial algebras, Algebra Universalis 29 (1992) 378-401, doi: 10.1007/BF01212439. Zbl0771.08001
- [8] T.R. Jensen and B. Toft, Graph Coloring Problems (Wiley-Interscience series in discrete mathematics and optimization, John Wiley & Sons Inc., 1995).
- [9] J. Kahn, Coloring nearly-disjoint hypergraphs with n+o(n) colors, J. Combin. Theory (A) 59 (1992) 31-39, doi: 10.1016/0097-3165(92)90096-D. Zbl0774.05073

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