To: Steve Krantz From: Doron Zeilberger Bcc: DZ's E-mailing list + Notices Editor A Copy is also posted as appendix to my Opinion 18 Re: Nah-Nah-Nah-Nugah, Guess Who is publishing in a `Substandard' Free Electronic Journal? Dear Steve, Please show the piece below to your retarded dean! In case you forgot, S. -T. Yau won the Fiedls Medal, (and Fan Chung should have!) Best wishes Doron ---------From ElJC------ From ejc@math.gatech.edu Fri Feb 12 09:36:02 1999 The following paper has been published in The Electronic Journal of Combinatorics: Fan Chung and S.-T. Yau Coverings, Heat Kernels and Spanning Trees It is R12 of Volume 6(1), and can be viewed at . Abstract: We consider a graph $G$ and a covering $\tilde{G}$ of $G$ and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite $k$-regular tree and we examine the heat kernels for general $k$-regular graphs. In particular, we show that a $k$-regular graph on $n$ vertices has at most \[ (1+o(1)) \frac {2\log n}{kn \log k} \left( \frac{(k-1)^{k-1}} {(k^2-2k)^{k/2-1}}\right)^n \] spanning trees, which is best possible within a constant factor. --------------------------------------------