The study of graph colouring has long been a central topic in discrete mathematics, with a prominent focus on optimising the assignment of labels or colours to vertices such that adjacent vertices are ...

The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G. We show that two specific ...

Vol. 12, No. 4, Dedicated to Professor Ko-Wei Lih on the Occasion of His 60th Birthday (July 2008), pp. 997-1005 (9 pages) The circular chromatic number χc(G) of a graph G is a very natural ...