Results 21 to 30 of about 2,394 (219)
Foundations of the chromatic polynomial
, 2022 The chromatic polynomial of a graph evaluated at λ gives the number of ways to properly color the graph with λ colors. It arose from the four color conjecture and in turn gave rise to the Tutte polynomial, which can be viewed as a two variable ...
Koh, Khee Meng, Dong, F. M.
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The game chromatic number of trees and forests [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then
Charles Dunn +4 more
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THE COMPLEXITY OF COMPUTING THE SIGN OF THE TUTTE POLYNOMIAL [PDF]
, 2014 (c) 2014 Society for Industrial and Applied ...
Jerrum, M, Goldberg, LA
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Chromatic Polynomials of Signed Book Graphs
Theory and Applications of Graphs, 2022 For $m \geq 3$ and $n \geq 1$, the $m$-cycle \textit{book graph} $B(m,n)$ consists of $n$ copies of the cycle $C_m$ with one common edge. In this paper, we prove that (a) the number of switching non-isomorphic signed $B(m,n)$ is $n+1$, and (b) the ...
Deepak Sehrawat, Bikash Bhattacharjya
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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
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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
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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
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Angewandte Chemie, EarlyView.Color‐pure all‐organic emitters, i.e., with narrow spectral characteristics, are intensively studied for high‐definition organic LEDs and multi‐color bioimaging. In order to guide targeted materials design, this educative review discusses spectral characteristics, proper definitions and units, and the physical basis of spectral broadening, to distill ...
Johannes Gierschner +6 more
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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
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On chromatic polynomials of hypergraphs
Electronic Notes in Discrete Mathematics, 2006 Abstract We consider a natural generalization of the chromatic polynomial of a graph. Let f ( x 1 , … , x m ) ( H , λ ) denote a number of different λ-colourings of a hypergraph H = ( X , E ) , X = { v 1 , … , v n } , E = { e 1 , … e m } , satisfying that in an edge e i
Ewa Drgas-Burchardt, Ewa Lazuka
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