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Bipartite Kneser graphs are Hamiltonian

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Mutze, Torsten and Su, Pascal (2017) Bipartite Kneser graphs are Hamiltonian. Combinatorica, 37 (6). pp. 1207-1219. doi:10.1007/s00493-016-3434-6

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Official URL: https://doi.org/10.1007/s00493-016-3434-6

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Abstract

For integers $k\geq 1$ and $n\geq 2k+1$ the Kneser graph $K(n,k)$ has as vertices all $k$-element subsets of $[n]:=\{1,2,\ldots,n\}$ and an edge between any two vertices (=sets) that are disjoint. The bipartite Kneser graph $H(n,k)$ has as vertices all $k$-element and $(n-k)$-element subsets of $[n]$ 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 $K(5,2)$ have a Hamilton cycle. The main contribution of this paper is proving this conjecture for bipartite Kneser graphs $H(n,k)$. We also establish the existence of cycles that visit almost all vertices in Kneser graphs $K(n,k)$ when $n=2k+o(k)$, generalizing and improving upon previous results on this problem.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Hypercube, Hamiltonian graph theory, Bipartite graphs
Journal or Publication Title: Combinatorica
Publisher: Springer
ISSN: 0209-9683
Official Date: December 2017
Dates:
DateEvent
December 2017Published
24 October 2016Available
14 November 2015Accepted
Volume: 37
Number: 6
Page Range: pp. 1207-1219
DOI: 10.1007/s00493-016-3434-6
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: This is a post-peer-review, pre-copyedit version of an article published in Combinatorica. The final authenticated version is available online at: https://doi.org/10.1007/s00493-016-3434-6
Access rights to Published version: Restricted or Subscription Access
Open Access Version:
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