The multichromatic numbers of some Kneser graphs
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The k th multichromatic number of the graph G is the least integer t such that the vertices of G can be assigned k -subsets of {1,2, …, t}, so that adjacent verticesof G receive disjoint sets.About:
This article is published in Discrete Mathematics.The article was published on 1998-04-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Kneser graph & Path graph.read more
Citations
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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
Covering arrays on graphs
Karen Meagher,Brett Stevens +1 more
TL;DR: A family of graphs QI(n, g) that have the property that there exists a CAN if and only if there is a homomorphism to QI(_, g), which defines a generalized colouring.
Journal Article
New hardness results for graph and hypergraph colorings.
TL;DR: In this article, it was shown that for all t ≥ 3, it is NP-hard to find a c-coloring of a t-colorable graph G with t colors when c ≤ 2t - 2.
Book ChapterDOI
Circuit double cover of graphs
TL;DR: The circuit double cover conjecture (CDC conjecture) is considered by most graph theorists as one of the major open problems in the field of graph theory as discussed by the authors, and it has been studied extensively.
Posted Content
On the locating chromatic number of Kneser graphs
Ali Behtoei,Behnaz Omoomi +1 more
TL;DR: In this paper, the authors studied the locating chromatic number of Kneser graphs, and showed that the minimum number of colors needed in a locating coloring of a connected graph is the number of colours needed to obtain a k-coloring of the graph.
References
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Journal ArticleDOI
Intersection theorems for systems of finite sets
Paul Erdös,Chao Ko,Richard Rado +2 more
TL;DR: In this article, the obliteration operator is used to remove from any system of elements the element above which it is placed, and the set of all systems (ao,av...,dn) such that avc[0,m); \av\ 1 (v < »),
Journal ArticleDOI
Kneser's conjecture, chromatic number, and homotopy
TL;DR: If the simplicial complex formed by the neighborhoods of points of a graph is (k − 2)-connected then the graph is not k-colorable, and Kneser's conjecture is proved, asserting that if all n-subsets of a (2n − k)-element set are divided into k + 1 classes, one of the classes contains two disjoint n- subsets.
Journal ArticleDOI
Some intersection theorems for systems of finite sets
A. J. W. Hilton,E. C. Milner +1 more
Journal ArticleDOI
The Complexity of Near-Optimal Graph Coloring
TL;DR: It is proved that even coming close to khgr;(G) with a fast algorithm is hard, and it is shown that if for some constant r < 2 and constant d there exists a polynomial-time algorithm A which guarantees A(G).