Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
The total chromatic number zt(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same colo...
This paper presents algorithms to find vertex-critical and edgecritical subgraphs in a given graph G, and demonstrates how these critical subgraphs can be used to determine the ch...
Christian Desrosiers, Philippe Galinier, Alain Her...
For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent t...
Hong-Jian Lai, Jianliang Lin, Bruce Montgomery, Ta...
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....