Copy the page URI to the clipboard
Hilton, A. J. W.; Holroyd, F. C. and Spencer, C. L.
(2010).
DOI: https://doi.org/10.1093/qmath/haq005
Abstract
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.
Viewing alternatives
Metrics
Public Attention
Altmetrics from AltmetricNumber of Citations
Citations from Dimensions- Request a copy from the author This file is not available for public download