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- W2952449103 abstract "For a graph G and integer rgeq 1 we denote the collection of independent r-sets of G by I^{(r)}(G). If vin V(G) then I_v^{(r)}(G) is the collection of all independent r-sets containing v. A graph G, is said to be r-EKR, for rgeq 1, iff no intersecting family Asubseteq I^{(r)}(G) is larger than max_{vin V(G)}|I^{(r)}_v(G)|. There are various graphs which are known to have this property: the empty graph of order ngeq 2r (this is the celebrated Erdos-Ko-Rado theorem), any disjoint union of at least r copies of K_t for tgeq 2, and any cycle. In this paper we show how these results can be extended to other classes of graphs via a compression proof technique. In particular we show that any disjoint union of at least r complete graphs, each of order at least two, is r-EKR. We also show that paths are r-EKR for all rgeq 1." @default.
- W2952449103 created "2019-06-27" @default.
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- W2952449103 date "2003-07-04" @default.
- W2952449103 modified "2023-09-27" @default.
- W2952449103 title "Compression and Erdos-Ko-Rado graphs" @default.
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