Results 41 to 50 of about 2,394 (219)
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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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
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Improved inclusion-exclusion identities via closure operators [PDF]
Discrete Mathematics & Theoretical Computer Science, 2000 Let (A v) v ∈ V be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure operator on the power set of V having the unique base property.
Klaus Dohmen
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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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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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The equivalence of two graph polynomials and a symmetric function
, 2009 The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any ...
Noble, SD +5 more
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On the chromatic number of (P_{5},windmill)-free graphs [PDF]
Opuscula Mathematica, 2017 In this paper we study the chromatic number of \((P_5, windmill)\)-free graphs. For integers \(r,p\geq 2\) the windmill graph \(W_{r+1}^p=K_1 \vee pK_r\) is the graph obtained by joining a single vertex (the center) to the vertices of \(p\) disjoint ...
Ingo Schiermeyer
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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
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The chromatic polynomial of fatgraphs and its categorification [PDF]
, 2006 We introduce a homology theory for embedded graphs whose graded Euler characteristic is the chromatic polynomial, and whose Poincaré polynomial is invariant on different planar embeddings of the same graph.
Martin Loebl +3 more
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Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts
Advances in Fuzzy Systems, 2019 Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc.
Mamo Abebe Ashebo +1 more
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