842 research outputs found
The eigenvalues of -Kneser graphs
In this note, we prove some combinatorial identities and obtain a simple form
of the eigenvalues of -Kneser graphs
Bipartite Kneser graphs are Hamiltonian
For integers and the Kneser graph has as vertices all -element subsets of and an edge between any two vertices (=sets) that are disjoint. The bipartite Kneser graph has as vertices all -element and -element subsets of and an edge between any two vertices where one is a subset of the other. It has long been conjectured that all Kneser graphs and bipartite Kneser graphs except the Petersen graph have a Hamilton cycle. The main contribution of this paper is proving this conjecture for bipartite Kneser graphs . We also establish the existence of cycles that visit almost all vertices in Kneser graphs when , generalizing and improving upon previous results on this problem
Resolving sets for Johnson and Kneser graphs
A set of vertices in a graph is a {\em resolving set} for if, for
any two vertices , there exists such that the distances . In this paper, we consider the Johnson graphs and Kneser
graphs , and obtain various constructions of resolving sets for these
graphs. As well as general constructions, we show that various interesting
combinatorial objects can be used to obtain resolving sets in these graphs,
including (for Johnson graphs) projective planes and symmetric designs, as well
as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems
and toroidal grids.Comment: 23 pages, 2 figures, 1 tabl
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