The Odd Girth of the Generalised Kneser Graph

LetX={1,2,..., n}be a set ofnelements and letX(r)be the collection of all the subsets ofXcontaining preciselyrelements. Then the generalised Kneser graphK(n,r,s)(when2r-s≤n)is the graph with vertex setX(r)and edgesABforA,B∈X(r)with ‖A∩B‖≤s.Here we show that the odd girth of the generalised Kneser gr...

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Published in:European journal of combinatorics 1997-08, Vol.18 (6), p.607-611
Main Author: Denley, Tristan
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Language:English
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description LetX={1,2,..., n}be a set ofnelements and letX(r)be the collection of all the subsets ofXcontaining preciselyrelements. Then the generalised Kneser graphK(n,r,s)(when2r-s≤n)is the graph with vertex setX(r)and edgesABforA,B∈X(r)with ‖A∩B‖≤s.Here we show that the odd girth of the generalised Kneser graphK(n,r, s)is 2⌈(r − s)/[n − 2(r − s)]⌉+1 provided thatnis large enough compared withrands.
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title The Odd Girth of the Generalised Kneser Graph
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