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

• Autorzy: Lucien Haddad , Claude Tardif
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 08A55: Partial algebras

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 3
• Strony: 545-549

Daty

wydano

2004

otrzymano

2004-07-12

Twórcy

autor

Lucien Haddad

• Department of Mathematics and Computer Science, Royal Military College of Canada, PO Box 17000, Station "Forces", Kingston, Ontario K7K 7B4 Canada

autor

Claude Tardif

• Department of Mathematics and Computer Science, Royal Military College of Canada, PO Box 17000, Station "Forces", Kingston, Ontario K7K 7B4 Canada

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1252