Lower Bounds and Upper Bounds for Chromatic Polynomials. Dohmen, K. J. Graph Theory, 17(1):75--80, 1993.
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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}
}
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