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)=∅ 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, Šparl and Žerovnik (2011) and improves the result of Sudeep and Vishwanathan (2005), who proved the existence of a 14-[6]coloring.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
