Results 1 to 10 of about 1,320 (180)
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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A Categorification for the Signed Chromatic Polynomial
The Electronic Journal of Combinatorics, 2022 By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph.
Zhiyun Cheng +3 more
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The chromatic polynomial of a graph [PDF]
Pacific Journal of Mathematics, 1985 First, the author summarizes some known results on chromatical polynomials and sketches their proofs. Then he lists the chromatical polynomials of all graphs with fewer than seven vertices.
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Discrete Mathematics, 1994 Let \(T_ G(\lambda)\) denote the number of \(T\)-colourings of graph \(G\) of order \(n\). The author shows that for each set \(T\) of nonnegative integers with maximal element \(r\), there is a polynomial \(Q_ G(\lambda)\) such that \(Q_ G(\lambda)= T_ G(\lambda)\) for all \(\lambda\geq r(n- 1)\).
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On the Roots of Chromatic Polynomials
Journal of Combinatorial Theory, Series B, 1998 A 2-tree is a graph constructed from \(K_2\) by successively joining a new vertex to both vertices of an existing edge. The author shows the following: (1) The chromatic polynomial of a connected graph with \(n\) vertices and \(m\) edges has a root with modulus at least \((m-1)/(n- 2)\).
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Approximating the Chromatic Polynomial
CoRR, 2016 Chromatic polynomials are important objects in graph theory and statistical physics, but as a result of computational difficulties, their study is limited to graphs that are small, highly structured, or very sparse. We have devised and implemented two algorithms that approximate the coefficients of the chromatic polynomial $P(G,x)$, where $P(G,k)$ is ...
Yvonne Kemper, Isabel Beichl
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Chromatically unique 6-bridge graph theta(a,a,a,b,b,c)
Electronic Journal of Graph Theory and Applications, 2016 For a graph $G$, let $P(G,\lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromatically unique if for any graph chromatically equivalent to $
N.S.A. Karim +2 more
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Generalized chromatic polynomials
Discrete Mathematics, 1984 In the study of combinatorics there are several polynomials used including Birkhoff's chromatic polynomial for graphs, the study of Stanley's order polynomial for partially ordered sets and Tutte's dichromatic polynomial for graphs. The author develops a common basis for these polynomials.
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A result on co-chromatic graphs
International Journal of Mathematics and Mathematical Sciences, 1981 A sufficient condition for two graphs with the same number of nodes to have the same chromatic polynomial is given.
E. J. Farrell
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Coloring Rings in Species [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a generalization of the chromatic polynomial, and chromatic symmetric function, arising in the study of combinatorial species. These invariants are defined for modules over lattice rings in species.
Jacob White
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