Results 101 to 110 of about 2,394 (219)
, 2022 The chromatic polynomial gives the number of proper λ-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.
G Farr (13134486), K Morgan (13134483)
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Hypergraphs with Pendant Paths are not Chromatically Unique
Discussiones Mathematicae Graph Theory, 2014 In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
Tomescu Ioan
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Approximating chromatic sum coloring of bipartite graphs in expected polynomial time
Труды Института системного программирования РАН, 2018 It is known that if P≠NP the sum coloring problem cannot be approximated within for some constant . We propose for arbitrary small an approximation scheme for this problem that works in expected polynomial time.
A. S. Asratian, N. N. Kuzyurin
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A generalization of the chromatic polynomial of a cycle [PDF]
Computer Science Journal of Moldova, 2005 We prove that if an edge of a cycle on vertices is extended by adding vertices, then the the chromatic polynomial of such generalized cycle is: $$P(H_k,\lambda)=(\lambda-1)^n\sum_{i=0}^k \lambda^i+(-1)^n(\lambda-1).$$
Julian A. Allagan
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Proof of a Chromatic Polynomial Conjecture
Journal of Combinatorial Theory, Series B, 2000 Let \(P(G,\lambda)\) be the chromatic polynomial of a graph \(G\) (i.e., the number of mappings \(f\) from the vertex set of \(G\) to \(\{1,2,\dots, \lambda\}\) such that \(f(x)\neq f(y)\) whenever \(x\) and \(y\) are adjacent vertices in \(G\) if \(\lambda\) is a positive integer).
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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).
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Transactions of the American Mathematical Society, 1946 Birkhoff, George D., Lewis, D. C.
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The chromatic polynomial of an unlabeled graph
, 1985 We investigate the chromatic polynomial χ(G, λ) of an unlabeled graph G. It is shown that χ(G, λ) = (1|A(g)|) Σπ ∈ A(g) χ(g, π, λ), where g is any labeled version of G, A(g) is the automorphism group of g and χ(g, π, λ) is the chromatic polynomial for ...
Hanlon, P
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Tutte's first colour-cycle conjecture
, 1975 Includes bibliographical references.This thesis presents a proof of Conjecture I (see Section 35) of W. T. Tutte's paper "A contribution to the theory of chromatic polynomials''.
Kilpatrick, Peter Allan
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Le Matematiche, 1992 In this paper, we give the maximal number of (k+r)-colouring of a graph with n vertices and chromatic number k. Also, we obtain the maximal values for chromatic polynomial of a graph.
Dănuţ Marcu
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