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International Journal of Mathematics and Mathematical Sciences
Volume 2014 (2014), Article ID 749856, 4 pages
http://dx.doi.org/10.1155/2014/749856
Research Article

A Note on the Warmth of Random Graphs with Given Expected Degrees

1Einstein Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
2Singapore University of Technology and Design, Singapore 138682

Received 1 February 2014; Revised 12 May 2014; Accepted 16 June 2014; Published 30 June 2014

Academic Editor: Imed Kacem

Copyright © 2014 Yilun Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the random graph model for a given expected degree sequence . Warmth, introduced by Brightwell and Winkler in the context of combinatorial statistical mechanics, is a graph parameter related to lower bounds of chromatic number. We present new upper and lower bounds on warmth of . In particular, the minimum expected degree turns out to be an upper bound of warmth when it tends to infinity and the maximum expected degree with .