Hilton, A. J. W.; Holroyd, F. C. and Spencer, C. L.
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|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1093/qmath/haq005|
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A graph G is r-starred if, for some , 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 -starred (where 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|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Fred Holroyd|
|Date Deposited:||17 Nov 2010 16:24|
|Last Modified:||12 Dec 2012 20:04|
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