The T-Tone Chromatic Number of Random Graphs
A proper 2-tone k-coloring of a graph is a labeling of the vertices with elements from (formula presented.) such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2-tone chromatic number of a graph G, denoted τ 2(G) is the smallest k such that G admits a proper 2-tone k coloring. In this paper, we prove that w.h.p. for (formula presented.) where X represents the ordinary chromatic number. For sparse random graphs with p = c/n, c constant, we prove that (formula presented.) where Δ represents the maximum degree. For the more general concept of t-tone coloring, we achieve similar results.
MSU Digital Commons Citation
Bal, Deepak; Bennett, Patrick; Dudek, Andrzej; and Frieze, Alan, "The T-Tone Chromatic Number of Random Graphs" (2014). Department of Mathematics Facuty Scholarship and Creative Works. 180.