{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T10:49:27Z","timestamp":1769856567606,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The vertex set of the Kneser graph $K(n,k)$ is $V = \\binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \\subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently determined by Alishahi and Taherkhani, whenever $n$ is large enough compared to $k$ and $F$. In this paper, we determine the second largest size of a vertex set $W \\subseteq V$ such that $K(n,k)[W]$ is $F$-free, in the case when $F$ is an even cycle or a complete multi-partite graph. In the latter case, we actually give a more general theorem depending on the chromatic number of $F$.\u00a0<\/jats:p>","DOI":"10.37236\/8130","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:07:57Z","timestamp":1578640077000},"source":"Crossref","is-referenced-by-count":2,"title":["Stability Results for Vertex Tur\u00e1n Problems in Kneser Graphs"],"prefix":"10.37236","volume":"26","author":[{"given":"D\u00e1niel","family":"Gerbner","sequence":"first","affiliation":[]},{"given":"Abhishek","family":"Methuku","sequence":"additional","affiliation":[]},{"given":"D\u00e1niel T.","family":"Nagy","sequence":"additional","affiliation":[]},{"given":"Balazs","family":"Patkos","sequence":"additional","affiliation":[]},{"given":"M\u00e1t\u00e9","family":"Vizer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,5,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p13\/7826","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p13\/7826","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:14:38Z","timestamp":1579234478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,3]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/8130","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,3]]},"article-number":"P2.13"}}