{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:44:06Z","timestamp":1759063446919,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Kneser graph $K(n,r)$ has as vertices all $r$-subsets of an $n$-set with two vertices adjacent if the corresponding subsets are disjoint. It is conjectured that, except for $K(5,2)$, these graphs are Hamiltonian for all $n\\geq 2r+1$. In this note we describe an inductive construction which relates Hamiltonicity of $K(2r+2s,r)$ to Hamiltonicity of $K(2r'+s,r')$. This shows  (among other things) that Hamiltonicity of $K(2r+1,r)$ for all $3\\leq r\\leq k$ implies Hamiltonicity of $K(2r+2,r)$ for all $r\\leq 2k+1$.  Applying this result extends the range of values for which Hamiltonicity of $K(n,r)$ is known.  Another consequence is that certain families of Kneser graphs ($K(\\frac{27}{13}r,r)$ for instance) contain infinitely many Hamiltonian graphs. <\/jats:p>","DOI":"10.37236\/676","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:41:38Z","timestamp":1578696098000},"source":"Crossref","is-referenced-by-count":8,"title":["An Inductive Construction for Hamilton Cycles in Kneser Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"J. Robert","family":"Johnson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,9,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p189\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p189\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:01:36Z","timestamp":1579284096000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p189"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/676","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,9,20]]},"article-number":"P189"}}