A linear time algorithm for 7-[3]coloring triangle-free hexagonal graphs

  • Authors:

  • Petra ŠParl;Rafał Witkowski;Janez Erovnik

  • Affiliations:

  • University of Maribor, Faculty of Organizational Sciences, Kidričeva 55a, SI-4000 Kranj, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia;Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Poznań, Poland;University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, SI-1000 Ljubljana, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

  • Venue:
  • Information Processing Letters
  • Year:
  • 2012

Quantified Score

Hi-index 0.89

Visualization

Abstract

Given a graph G and p@?N, a proper n-[p]coloring is a mapping f:V(G)-2^{^1^,^...^,^n^} such that |f(v)|=p for any vertex v@?V(G) and f(v)@?f(u)=@A for any pair of adjacent vertices u and v. An n-[p]coloring is a special case of a multicoloring. Finding a multicoloring of induced subgraphs of the triangular lattice (called hexagonal graphs) has important applications in cellular networks. In this article we provide an algorithm to find a 7-[3]coloring of triangle-free hexagonal graphs in linear time, without using the four-color theorem, which solves the open problem stated by Sau, Sparl and Zerovnik (2011) and improves the result of Sudeep and Vishwanathan (2005), who proved the existence of a 14-[6]coloring.