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math.CO2003
Compression and Erdos-Ko-Rado graphs
Fred Holroyd, John Talbot
For a graph G and integer r\geq 1 we denote the collection of independent r-sets of G by I^{(r)}(G). If v\in V(G) then I_v^{(r)}(G) is the collection of all independent r-sets cont…
math.CO2003
The number of k-intersections of an intersecting family of r-sets
John Talbot
The Erdos-Ko-Rado theorem tells us how large an intersecting family of r-sets from an n-set can be, while results due to Lovasz and Tuza give bounds on the number of singletons tha…
math.CO2002
Intersecting Families of Separated Sets
John Talbot
We prove a conjecture due to Holroyd and Johnson that an analogue of the Erdos-Ko-Rado theorem holds for k-separated sets. In particular this determines the independence number of…