Some Partial Results on Hadwiger's Conjecture
by
Zi-Xia Song
Department of Mathematics, University of Central Florida

Let D=(d₁, d₂, ..., d_n) be a graphic sequence with 0 ≤ d₁ ≤ d₂ ≤ ... ≤ d_n. 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. We say that D is H-free if no graph in R[D] contains H as an induced subgraph. We prove that Hadwiger's Conjecture is true for graphs whose degree sequences are claw-free or K₁∪K₃-free.

Date received: April 27, 2009