Ordered coloring grids and related graphs

Authors:
Amotz Bar-Noy;Panagiotis Cheilaris;Michael Lampis;Valia Mitsou;Stathis Zachos
Affiliations:
Computer and Information Science Department Brooklyn College, City University of New York, Brooklyn, NY;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary;Doctoral Program in Computer Science The Graduate Center, City University of New York, New York;Doctoral Program in Computer Science The Graduate Center, City University of New York, New York;Computer and Information Science Department Brooklyn College, City University of New York, Brooklyn, NY
Venue:
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Year:
2009

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Abstract

We investigate a coloring problem, called ordered coloring, in grids and some other families of grid-like graphs. Ordered coloring (also known as vertex ranking) is related to conflict-free coloring and other traditional coloring problems. Such coloring problems can model (among others) efficient frequency assignments in cellular networks. Our main technical results improve upper and lower bounds for the ordered chromatic number of grids and related graphs. To the best of our knowledge, this is the first attempt to calculate exactly the ordered chromatic number of these graph families.