Geodesic
A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 545-549.

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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.
Keywords: chromatic number, Erdős-Faber-Lovász conjecture, maximal partial clones 
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Haddad, Lucien; Tardif, Claude. A clone-theoretic formulation of the Erdos-Faber-Lovász conjecture. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 545-549. http://geodesic.mathdoc.fr/item/DMGT_2004_24_3_a16/

[1] P. Erdős, On the Combinatorial problems which I would most like to see solved, Combinatorica 1 (1981) 25-42, doi: 10.1007/BF02579174.

[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.

[4] L. Haddad, Maximal partial clones determined by quasi-diagonal relations, J. Inf. Process. Cybern. EIK 24 (1988) 7/8 355-366.

[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.

[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.

[7] L. Haddad and I.G. Rosenberg, Completeness theory for finite partial algebras, Algebra Universalis 29 (1992) 378-401, doi: 10.1007/BF01212439.

[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.