A new construction technique of a triangle-free 3-colored K16’s

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Author Jaam, Jihad Mohamad en_US
Available date 2009-12-30T05:59:39Z en_US
Publication Date 2006-12-03 en_US
Publication Name Information Sciences
Identifier http://dx.doi.org/10.1016/j.ins.2006.12.002
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 1992-1995 en_US
URI http://hdl.handle.net/10576/10577 en_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 en en_US
Publisher Elsevier Inc en
Subject Multicolor Ramsey number en_US
Subject Satisfiability en_US
Subject Graph en_US
Title A new construction technique of a triangle-free 3-colored K16’s en_US
Type Article en_US

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