Journal ArticleDOI
Star chromatic number
TLDR
A generalization of the chromatic number of a graph is introduced such that the colors are integers modulo n, and the colors on adjacent vertices are required to be as far apart as possible.Abstract:
A generalization of the chromatic number of a graph is introduced such that the colors are integers modulo n, and the colors on adjacent vertices are required to be as far apart as possible.read more
Citations
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Journal ArticleDOI
A survey of Nordhaus-Gaddum type relations
Mustapha Aouchiche,Pierre Hansen +1 more
TL;DR: In this paper, Nordhaus and Gaddum gave lower and upper bounds on the sum and product of the chromatic number of a graph and its complement, in terms of the order of the graph.
Journal ArticleDOI
Graph labeling and radio channel assignment
TL;DR: In this paper, the authors consider the problem of finding labelings of minimum span, given a graph and a set of constraints, and obtain optimal labelings for up to three levels of constraint.
Book ChapterDOI
Graph homomorphisms: structure and symmetry
Geňa Hahn,Claude Tardif +1 more
TL;DR: The first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey can be found in this paper, where the basic definitions, examples and uses of homomorphisms are discussed.
Journal ArticleDOI
A note on the star chromatic number
J. A. Bondy,Pavol Hell +1 more
TL;DR: A.A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest, and his work relies on continuous methods.
Habilitation a diriger des recherches
L’Étude Mathématique,De Quelques Modèles,Issus De La,Physique Statistique,Hors Équilibre,Stéphane Mischler,En Mathématiques,Pierre Degond,Laurent Desvillettes,François Golse,Otared Kavian,Benoît Perthame,Jean-Pierre Puel,Mario Pulvirenti,Mais la vache,savait nager +15 more
TL;DR: Granvorka et al. as discussed by the authors present le Ceregmia de Travail, le document de travail published en 2010 by the International Association of Christians and Jews (IAC) in Haiti.
References
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Journal ArticleDOI
n-Tuple colorings and associated graphs
TL;DR: In this paper, the n-tuple graph coloring is defined together with its respective chromatic number xn, and it is proved that these numbers satisfy the inequality xn ≥ 2 + xn−1, and that equality holds only for bipartite graphs.
Journal ArticleDOI
A (<5)-Colour Theorem for Planar Graphs
Journal ArticleDOI
r-tuple colorings of uniquely colorable graphs
TL;DR: It is shown that this cannot happen for n=3 and r=2 and that for a given n and r to establish the conjecture that no uniquely n-colorable graph can receive an r-tuple coloring from fewer than nr colors it suffices to prove it for on a finite set of uniquely n -colorable graphs.