Circular colouring and algebraic no-homomorphism theorems

Authors:
Amir Daneshgar;Hossein Hajiabolhassan
Affiliations:
Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran;Department of Mathematics, Shahid Beheshti University, P.O. Box 19834, Tehran, Iran
Venue:
European Journal of Combinatorics
Year:
2007

Citing 4
Cited 1

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Circular chromatic number: a survey

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Graph homomorphisms through random walks

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On the isoperimetric spectrum of graphs and its approximations

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Abstract

In this paper, we apply some new algebraic no-homomorphism theorems in conjunction with some new chromatic parameters to estimate the circular chromatic number of graphs. To show the applicability of the general results, as a couple of examples, we generalize a well known inequality for the fractional chromatic number of graphs and we also show that the circular chromatic number of the graph obtained from the Petersen graph by excluding one vertex is equal to 3. Also, we focus on the Johnson-Holroyd-Stahl conjecture about the circular chromatic number of Kneser graphs and we propose an approach to this conjecture. In this regard, we introduce a new related conjecture on Kneser graphs and we also provide some supporting evidence.