Results 31 to 40 of about 2,394 (219)
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
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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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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
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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
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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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Chromatic polynomials of hypergraphs
Applied Mathematics Letters, 2007 The authors investigate the number of \(\lambda\)-colourings of the vertices of a hypergraph \(H\) such that each edge \(e_i\) of \(H\) contains at least \(x_i\) differently coloured vertices for given quantities \(x_1,\dots,x_m\) (one for each edge).
Ewa Drgas-Burchardt, Ewa Lazuka
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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
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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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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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