Ordered coloring of grids and related graphs I
Amotz Bar-Noy, Panagiotis Cheilaris, Michael Lampis, Valia Mitsou, Stathis Zachos · 2010
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 e cient 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.