Problems on chromatic polynomials of hypergraphs

This paper is a continuation of the Waterloo Research Report CORR 81-12, (see [1]) referred to in what follows as I. That Report is entitled “Chromatic Solutions”. It is largely concerned with a power series h in a variable z2, in which the coefficients are polynomials in a “colour number” λ. By definition the coefficient of z2r, where r > 0, is the sum of the chromatic polynomials of the rooted planar triangulations of 2r faces. (Multiple joins are allowed in these triangulations.) Thus for a positive integral λ the coefficient is the number of λ-coloured rooted planar triangulations of 2r faces. The use of the symbol z2 instead of a simple letter t is for the sake of continuity with earlier papers.In I we consider the case(1)where n is an integer exceeding 4.

Download Full-text

Inequalities on Chromatic Polynomials

Chromatic Polynomials and Chromaticity of Graphs ◽

10.1142/9789812569462_0015 ◽

2005 ◽

pp. 309-326

Keyword(s):

Chromatic Polynomials

Download Full-text

Chromatic polynomials of homeomorphism classes of graphs

Discrete Mathematics ◽

10.1016/s0012-365x(98)00378-1 ◽

1999 ◽

Vol 204 (1-3) ◽

pp. 337-356 ◽

Cited By ~ 31

Author(s):

Ronald C. Read ◽

Earl Glen Whitehead

Keyword(s):

Chromatic Polynomials

Download Full-text

Zero-free intervals of chromatic polynomials of hypergraphs

Discrete Mathematics ◽

10.1016/j.disc.2020.112134 ◽

2020 ◽

Vol 343 (12) ◽

pp. 112134

Author(s):

Ruixue Zhang ◽

Fengming Dong

Keyword(s):

Chromatic Polynomials

Download Full-text

Location of Zeros of Chromatic and Related Polynomials of Graphs

Canadian Journal of Mathematics ◽

10.4153/cjm-1994-002-3 ◽

1994 ◽

Vol 46 (1) ◽

pp. 55-80 ◽

Cited By ~ 40

Author(s):

Francesco Brenti ◽

Gordon F. Royle ◽

David G. Wagner

Keyword(s):

Generating Functions ◽

Sufficient Conditions ◽

Combinatorial Identities ◽

Chromatic Polynomials ◽

Real Zeros ◽

Location Of Zeros ◽

Theoretical Results

AbstractWe 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.

Download Full-text