Lower Bounds and Upper Bounds for Chromatic Polynomials. Dohmen, K. J. Graph Theory, 17(1):75--80, 1993. doi abstract bibtex In this paper we give lower bounds and upper bounds for chromatic polynomials of simple undirected graphs on $n$ vertices having $m$ edges and girth exceeding $g$.
@article{ Dohmen:1993:LBU,
author = {Klaus Dohmen},
title = {Lower Bounds and Upper Bounds for Chromatic Polynomials},
journal = {J. Graph Theory},
year = {1993},
volume = {17},
number = {1},
pages = {75--80},
doi = {10.1002/jgt.3190170109},
abstract = {In this paper we give lower bounds and upper bounds for
chromatic polynomials of simple undirected graphs on $n$
vertices having $m$ edges and girth exceeding $g$.},
keywords = {graph, chromatic polynomial, bounds}
}