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Author Jaam, Jihad Mohamaden_US
Available date 2009-12-30T05:59:39Zen_US
Publication Date 2006-12-03en_US
Publication Name Information Sciences
Citation Jihad Mohamad Jaam, A new construction technique of a triangle-free 3-colored K16’s, Information Sciences, Volume 177, Issue 9, 1 May 2007, Pages 1992-1995en_US
URI http://dx.doi.org/10.1016/j.ins.2006.12.002en_US
URI http://hdl.handle.net/10576/10577en_US
Abstract In this paper, we propose a new coloring technique of the edges of the complete graph on 16 vertices, K16, with three different colors, without producing any monochromatic triangle. This method is totally different from those proposed by [R.E. Greenwood, A.M. Gleason, Combinatorial relations and chromatic graphs, Canadian Journal of Mathematics 7 (1955) 1–7; J.G. Kalbfleish, R.G. Stanton, On the maximal triangle-free edge-chromatic graphs in three colors, Journal of Combinatorial Theory 5 (1968) 9–20; C. Laywine, L.P. Mayberry, A simple construction giving the two non-isomorphic triangle free 3-colored K16’s, Journal of Combinatorial Theory Series B (1988) 120–124; B. Benhamou, Étude des Symétries et de la Cardinalité en Calcul Propoaitionel: Application aux Algorithmes Syntaxiques, Ph.D. Thesis, University of Aix-Marseilles I, France, 1993] which prove that the classical multicolor Ramsey number R(3, 3, 3) is 17. This number is the only non-trivial tricolor Ramsey number known till now in spite of more than fifty years of extensive research on Ramsey numbers [S.P. Radziszowski, Small Ramsey numbers, The Electronic Journal of Combinatorics DS1.Revision 11 (2006) 1–60]. We show also how we can convert the Ramsey-graph 3-coloring problem into a satisfiability instance having 2160 clauses of 3-literals each and 360 variables (i.e., a 3-SAT instance).en_US
Language enen_US
Publisher Elsevier Incen
Subject Multicolor Ramsey numberen_US
Subject Satisfiabilityen_US
Subject Graphen_US
Title A new construction technique of a triangle-free 3-colored K16’sen_US
Type Articleen_US


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