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Chromatic Polynomials of Mixed Hypercycles
Discussiones Mathematicae Graph Theory, 2014 We color the vertices of each of the edges of a C-hypergraph (or cohypergraph) in such a way that at least two vertices receive the same color and in every proper coloring of a B-hypergraph (or bihypergraph), we forbid the cases when the vertices of any ...
Allagan Julian A., Slutzky David
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Chromatic Polynomials Of Some (m,l)-Hyperwheels [PDF]
Computer Science Journal of Moldova, 2014 In this paper, using a standard method of computing the chromatic polynomial of hypergraphs, we introduce a new reduction theorem which allows us to find explicit formulae for the chromatic polynomials of some (complete) non-uniform $(m,l)-$hyperwheels ...
Julian A. Allagan
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Connections between the matching and chromatic polynomials
International Journal of Mathematics and Mathematical Sciences, 1992 The main results established are (i) a connection between the matching and chromatic polynomials and (ii) a formula for the matching polynomial of a general complement of a subgraph of a graph.
E. J. Farrell, Earl Glen Whitehead
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, 2023 This thesis studies the chromatic polynomial Z(G;q) and its generalizaton, the partition function Z(G;q,y) of the random cluster (RC) model. The main questions concern the location of the zeros of the chromatic polynomial, and the algorithmic approximation of the RC partition function.Chapter 2 studies the chromatic zeros of series-parallel graphs and ...
Hunski, Fran
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Certificates of Factorisation for Chromatic Polynomials
The Electronic Journal of Combinatorics, 2009 The chromatic polynomial gives the number of proper $\lambda$-colourings of a graph $G$. This paper considers factorisation of the chromatic polynomial as a first step in an algebraic study of the roots of this polynomial. The chromatic polynomial of a graph is said to have a chromatic factorisation if $P({G},\lambda)=P({H_{1}},\lambda)P({H_{2 ...
Kerri Morgan, Graham Farr
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DP color functions versus chromatic polynomials (II) [PDF]
Journal of Graph Theory, 2022 For any connected graph G $G$ , let P(G,m) $P(G,m)$ and PDP(G,m) ${P}_{DP}(G,m)$ denote the chromatic polynomial and Dvořák and Postle (DP) color function of G $G$ , respectively. It is known that PDP(G,m)≤P(G,m) ${P}_{DP}(G,m)\le P(G,m)$ holds for every
Meiqiao Zhang, Fengming Dong
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DP color functions versus chromatic polynomials [PDF]
Advances in Applied Mathematics, 2021 For any graph $G$, the chromatic polynomial of $G$ is the function $P(G,m)$ which counts the number of proper $m$-colorings of $G$ for each positive integer $m$.
F. Dong, Yan Yang
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, 1994 In this thesis, we shall investigate chromatic polynomials of graphs, and some related polynomials. In Chapter 1, we study the chromatic polynomial written in a modified form, and use these results to characterise the chromatic polynomials of polygon trees. In Chapter 2, we consider the chromatic polynomial written as a sum of the chromatic polynomials
Tommy R Jensen, Bjarne Toft
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Chromatic polynomials of generalized trees
Discrete Mathematics, 1988 This short note surveys some recent results on chromatic polynomials of graphs built up in a treelike manner of q-cliques (yieldig q-trees) or of n-gons (n-gon-trees).
Whitehead, Earl Glen
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