The Open UniversitySkip to content

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.

Full text available as:
Full text not publicly available
Due to copyright restrictions, this file is not available for public download
Click here to request a copy from the OU Author.
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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
Share this page:


Scopus Citations

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340