Results 31 to 40 of about 1,320 (180)
Chromatic roots as algebraic integers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 A chromatic root is a zero of the chromatic polynomial of a graph. At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known ...
Adam Bohn
doaj +1 more source
Ultimate chromatic polynomials
Discrete Mathematics, 1994 An approach to enumeration problems relying on the algebra of free abelian groups is outlined. The main application is a generalization of the chromatic polynomial of a simple graph \(G\) to the ``ultimate chromatic polynomial'', which lies in the free abelian group generated by the poset \(K(G)\) of contractions of \(G\), and which reduces to the ...
Nigel Ray, William Schmitt
openaire +1 more source
The limit of chromatic polynomials
Journal of Combinatorial Theory, Series B, 1979 AbstractWe consider the large size limit of the number of q-colourings for three types of planar graph and obtain expansions for this limit in powers of (q − 1)−1. The methods used to derive and investigate these series are related to more general methods of investigating the Tutte polynomial used in theoretical physics.
D. Kim, Ian G. Enting
openaire +2 more sources
Note on chromatic polynomials of the threshold graphs
Electronic Journal of Graph Theory and Applications, 2019 Let G be a threshold graph. In this paper, we give, in first hand, a formula relating the chromatic polynomial of Ḡ (the complement of G) to the chromatic polynomial of G.
Noureddine Chikh, Miloud Mihoubi
doaj +1 more source
On chromatic equivalence of a pair of K_{4}-homeomorphs [PDF]
Opuscula Mathematica, 2010 Let \(P(G, \lambda)\) be the chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are said to be chromatically equivalent, denoted \(G \sim H\), if \(P(G, \lambda) = P(H, \lambda)\). We write \([G] = \{H| H \sim G\}\).
S. Catada-Ghimire, H. Roslan, Y. H. Peng
doaj +1 more source
Chromatic polynomials of hypergraphs
Discussiones Mathematicae Graph Theory, 2000 Let \(q\geq 2\) and \(H_{q,q+1}^{n}\) be the \((q+1)\)-uniform hypergraph having vertex set \(X\) with \(|X|=n \geq q+1\) and edge set consisting of all sets \(Y\cup \{x_{i}\}\) for \(1\leq i\leq n-q \), where \(Y\subset X\), \(|Y|=q\) and \(\{x_{1},\ldots ,x_{n-q}\}\cup Y=X\).
Mieczyslaw Borowiecki, Ewa Lazuka
openaire +2 more sources
ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS
Ural Mathematical Journal, 2021 Let \(P(G, x)\) be a chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are called chromatically equivalent iff \(P(G, x) = H(G, x)\). A graph \(G\) is called chromatically unique if \(G\simeq H\) for every \(H\) chromatically equivalent ...
Pavel A. Gein
doaj +1 more source
The computation of chromatic polynomials
Discrete Mathematics, 1999 The computation of the chromatic polynomial of the truncated icosahedron (a cubic planar graph with 60 vertices and 90 edges) is computed by enhancing the algorithm based on the classical delete-contract theorem.
Gary Haggard, Thomas R. Mathies
openaire +2 more sources
Chromatic Polynomials of Simplicial Complexes [PDF]
Graphs and Combinatorics, 2015 We consider s-chromatic polynomials of simplicial complexes, higher dimensional analogues of chromatic polynomials for graphs.
Møller, Jesper Michael, Nord, Gesche
openaire +5 more sources
On Weakly Distinguishing Graph Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A univariate graph polynomial P(G;X) is weakly distinguishing if for almost all finite graphs G there is a finite graph H with P(G;X)=P(H;X). We show that the clique polynomial and the independence polynomial are weakly distinguishing.
Johann A. Makowsky, Vsevolod Rakita
doaj +1 more source