{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:12:39Z","timestamp":1758823959693,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>This paper considers an infection spreading in a graph; a vertex gets infected if at least two of its neighbors are infected. The $P_3$-hull number is the minimum size of a vertex set that eventually infects the whole graph.\r\nIn the specific case of the Kneser graph $K(n,k)$, with $n\\ge 2k+1$, an infection spreading on the family of $k$-sets of an $n$-set is considered. A set is infected whenever two sets disjoint from it are infected. We compute the exact value of the $P_3$-hull number of $K(n,k)$ for $n&gt;2k+1$. For $n = 2k+1$, using graph homomorphisms from the Knesser graph to the Hypercube, we give lower and upper bounds.<\/jats:p>","DOI":"10.37236\/9903","type":"journal-article","created":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T01:17:40Z","timestamp":1627607860000},"source":"Crossref","is-referenced-by-count":1,"title":["On the $P_3$-Hull Number of Kneser Graphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Luciano N.","family":"Grippo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adri\u00e1n","family":"Pastine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo","family":"Torres","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario","family":"Valencia-Pabon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan C.","family":"Vera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,7,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T01:17:40Z","timestamp":1627607860000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/9903","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,7,30]]},"article-number":"P3.32"}}