We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
Let G be a undirected connected graph. Given a set of g groups each being a subset of V (G), tree routing and coloring is to produce g trees in G and assign a color to each of them...
Abstract. The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, it is known that k-color...
We develop new structural results for apex-minor-free graphs and show their power by developing two new approximation algorithms. The first is an additive approximation for colorin...
Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ich...
Coloring the nodes of a graph with a small number of colors is one of the most fundamental problems in theoretical computer science. In this paper, we study graph coloring in a di...