Results 191 to 200 of about 2,394 (219)

Counting packings of list-colorings of graphs

Enumerative Combinatorics and Applications
Hemanshu Kaul, Jeffrey A. Mudrock
doaj   +1 more source

Graphs with chromatic polynomial ∑l⩽m0lm0−l(λ)l

Discrete Mathematics, 2002
In this paper, using the properties of chromatic polynomial and adjoint polynomial, we characterize all graphs having chromatic polynomial ∑l⩽m0lm0−l(λ ...
Chengfu Ye
exaly   +2 more sources

On chromatic and flow polynomial unique graphs

Discrete Applied Mathematics, 2008
It is known that the chromatic polynomial and flow polynomial of a graph are two important evaluations of its Tutte polynomial, both of which contain much information of the graph.
Haidong Wu, Qinglin Yu
exaly   +2 more sources

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On the chromatic polynomial of a graph

Mathematical Programming, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
AVIS D., DE SIMONE C., NOBILI, Paolo
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Cutpoints and the chromatic polynomial

Journal of Graph Theory, 1984
AbstractWe prove that the multiplicity of the root 1 in the chromatic polynomial of a simple graph G is equal to the number of nontrivial blocks in G. In particular, a connected simple graph G has a cutpoint if and only if its chromatic polynomial is divisible by (λ – 1)2.
Earl Glen Whitehead Jr., Lian-Chang Zhao
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The chromatic polynomial and list colorings

Journal of Combinatorial Theory Series B, 2009
We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the ...
Carsten Thomassen
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Extended Chromatic Polynomials

Canadian Journal of Mathematics, 1972
Let G be a finite graph with non-empty vertex set (G) and edge set (G) (see [2]). Let λ be a positive integer. Tutte [5] defines a λ-colouring of G as a mapping of (G) into the set Iλ = {1, 2, 3, …, λ} with the property that two ends of any edge are mapped onto distinct integers.
Sobczyk, Andrew, Gettys, James O. jun.
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Chromatic Polynomials and the Symmetric Group

Graphs and Combinatorics, 2004
The author gives a new combinatorial interpretation of the coefficients of chromatic polynomials of graphs in terms of subsets of permutations and introduces a combinatorially defined polynomial associated to a directed graph. He proves that it is related to the chromatic polynomials.
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On injective chromatic polynomials of graphs

Discrete Mathematics, Algorithms and Applications, 2015
The injective chromatic number χi(G) [G. Hahn, J. Kratochvil, J. Siran and D. Sotteau, On the injective chromatic number of graphs, Discrete Math. 256(1–2) (2002) 179–192] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors.
Anjaly Kishore, M. S. Sunitha
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Chromatic polynomials and ?-polynomials

Journal of Graph Theory, 1996
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