Journal ArticleDOI
A note on the star chromatic number
J. A. Bondy,Pavol Hell +1 more
TLDR
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.Abstract:
A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make some simple observations that lead to a purely combinatorial treatment. Our methods yield shorter proofs and offer further insight.read more
Citations
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Book
Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical 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
Nowhere-zero 3-flows and modulo k-orientations
TL;DR: The main theorem of this paper provides partial results on some major open problems in graph theory, such as [email protected]?s 3-flow conjecture that every 4-edge connected graph admits a nowhere-zero 3- flow.
Book
Erdős-Ko-Rado Theorems: Algebraic Approaches
Chris Godsil,Karen Meagher +1 more
TL;DR: The Erdos-Ko-Rado Theorem as discussed by the authors is a well-known result in representation theory, and the Grassmann and Hamming schemes have been used to represent symmetric groups.
References
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Journal ArticleDOI
On the complexity of H -coloring
Pavol Hell,Jaroslav Nešetřil +1 more
TL;DR: The natural conjecture, formulated in several sources, asserts that the H-coloring problem is NP-complete for any non-bipartite graph H, and a proof of this conjecture is given.
Journal ArticleDOI
Star chromatic number
TL;DR: 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.
Journal ArticleDOI
Homomorphisms of 3-chromatic graphs
TL;DR: The principal result (Theorem 2) provides necessary conditions for the existence of a homomorphism onto a prescribed target and it is shown that iterated cartesian products of the Petersen graph form an infinite family of vertex transitive graphs no one of which is the homomorphic image of any other.