Hadwiger Number And Chromatic Number For Near Regular Degree Sequences

We consider a problem related to Hadwiger\u27s Conjecture. Let D=(d 1, d 2,...,d n) be a graphic sequence with 0≤d 1≤d 2≤···≤d n≤n-1. Any simple graph G with D its degree sequence is called a realization of D. Let R[D] denote the set of all realizations of D. Define h(D) = max{h(G): G∈R[D]} and χ(D) = max{χ(G):G∈R[D]}, where h(G) and χ(G) are Hadwiger number and chromatic number of a graph G, respectively. Hadwiger\u27s Conjecture implies that h(D)≥χ(D). In this paper, we establish the above inequality for near regular degree sequences. © 2009 Wiley Periodicals, Inc