Ordered coloring of grids and related graphs

Authors:
Amotz Bar-Noy;Panagiotis Cheilaris;Michael Lampis;Valia Mitsou;Stathis Zachos
Affiliations:
Brooklyn College, City University of New York, 2900 Bedford Avenue, Brooklyn, NY 11210, USA and Graduate Center, City University of New York, 365 5th Avenue, New York, NY 10016, USA;Center for Advanced Studies in Mathematics, Ben-Gurion University, Beer Sheva 84105, Israel;Graduate Center, City University of New York, 365 5th Avenue, New York, NY 10016, USA;Graduate Center, City University of New York, 365 5th Avenue, New York, NY 10016, USA;Brooklyn College, City University of New York, 2900 Bedford Avenue, Brooklyn, NY 11210, USA and Graduate Center, City University of New York, 365 5th Avenue, New York, NY 10016, USA and National T ...
Venue:
Theoretical Computer Science
Year:
2012

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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) has applications, among other areas, in efficient solving of sparse linear systems of equations and scheduling parallel assembly of products. Our main technical results improve upper and lower bounds for the ordered chromatic number of grids and related graphs.