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Location of Zeros of Chromatic and Related Polynomials of Graphs

Published online by Cambridge University Press:  20 November 2018

Francesco Brenti ,
Gordon F. Royle  and
David G. Wagner
Francesco Brenti
Affiliation:
Dipartimento di Matematica Universita' di Perugia Via Vanvitelli 1 1-06123, Perugia Italy
Gordon F. Royle
Affiliation:
Department of Computer Science University of Western Australia Perth, Western Australia Australia
David G. Wagner
Affiliation:
Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1
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Abstract

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We consider the location of zeros of four related classes of polynomials, one of which is the class of chromatic polynomials of graphs. All of these polynomials are generating functions of combinatorial interest. Extensive calculations indicate that these polynomials often have only real zeros, and we give a variety of theoretical results which begin to explain this phenomenon. In the course of the investigation we prove a number of interesting combinatorial identities and also give some new sufficient conditions for a polynomial to have only real zeros.

Keywords

05C1505A1530C1526C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 1 , 01 February 1994 , pp. 55 - 80
Copyright
Copyright © Canadian Mathematical Society 1994

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