A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest...
Vikraman Arvind, Christine T. Cheng, Nikhil R. Dev...
This paper introduces a new strategy for playing the marking game on graphs. Using this strategy, we prove that if G is a planar graph, then the game colouring number of G, and he...
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...
A k-track drawing is a crossing-free 3D straight-line drawing of a graph G on a set of k parallel lines called tracks. The minimum value of k for which G admits a k-track drawing ...
This paper discusses the game colouring number of partial k-trees and planar graphs. Let colg(PT k) and colg(P) denote the maximum game colouring number of partial k trees and the...