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No-hole 2-distant colorings for Cayley graphs on finitely generated abelian groups |
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| Authors: | Gerard J Chang Changhong Lu Sanming Zhou |
| Institution: | a Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan b National Center for Theoretical Sciences, Taipei Office, Taiwan c Department of Mathematics, East China Normal University, Shanghai 200062, PR China d Department of Mathematics and Statistics, The University of Melbourne, Parkville, Vic 3010, Australia e Institute of Theoretical Computing East China Normal University, Shanghai 200062, PR China f Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan |
| Abstract: | A no-hole 2-distant coloring of a graph Γ is an assignment c of nonnegative integers to the vertices of Γ such that |c(v)-c(w)|?2 for any two adjacent vertices v and w, and the integers used are consecutive. Whenever such a coloring exists, define nsp(Γ) to be the minimum difference (over all c) between the largest and smallest integers used. In this paper we study the no-hole 2-distant coloring problem for Cayley graphs over finitely generated abelian groups. We give sufficient conditions for the existence of no-hole 2-distant colorings of such graphs, and obtain upper bounds for the minimum span nsp(Γ) by using a group-theoretic approach. |
| Keywords: | Channel assignment T-coloring No-hole 2-distant coloring Cayley graph |
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