King Arthur and his knights with two round tables

Hilton, A. J. W.; Holroyd, F. C. and Spencer, C. L. (2010). King Arthur and his knights with two round tables. The Quarterly Journal of Mathematics, 62(3), pp. 625–635.

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DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.1093/qmath/haq005
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Abstract

A graph G is r-starred if, for some $v \in V(G)$ , a largest pairwise intersecting family of independent r-subsets of V(G) may be obtained by taking all such subsets containing v (the 'r-star' at v). Let G be the disjoint union of powers of cycles; Hilton and Spencer have studied the problem of determining the values of r for which G is r-starred. They conjectuerd that the property holds for all r, and made a weaker conjecture that this is so for the union of just two cycles. In this paper we prove the second conjectuer, showing also that if G is the unionj of several graphs, each a power of a cycle, then G is $\alpha$ -starred (where $\alpha$ is the independence number of G), provided that there is a homomorphism from some component of G to each of the other components.

Item Type:	Journal Article
Copyright Holders:	2010 Oxford University Press
ISSN:	0033-5606
Academic Unit/Department:	Mathematics, Computing and Technology > Mathematics and Statistics
Item ID:	24725
Depositing User:	Fred Holroyd
Date Deposited:	17 Nov 2010 16:24
Last Modified:	12 Dec 2012 20:04
URI:	http://oro.open.ac.uk/id/eprint/24725

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