{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T22:42:36Z","timestamp":1780785756848,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider, for every positive integer $a$, probability distributions on subsets of vertices of a graph with the property that every vertex belongs to the random set sampled from this distribution with probability at most $1\/a$. Among other results, we prove that for every positive integer $a$ and every planar graph $G$, there exists such a probability distribution with the additional property that for any set $X$ in the support of the distribution, the graph $G-X$ has component-size at most $(\\Delta(G)-1)^{a+O(\\sqrt{a})}$, or treedepth at most $O(a^3\\log_2(a))$. We also provide nearly-matching lower bounds.<\/jats:p>","DOI":"10.37236\/8909","type":"journal-article","created":{"date-parts":[[2020,10,21]],"date-time":"2020-10-21T04:05:38Z","timestamp":1603253138000},"source":"Crossref","is-referenced-by-count":6,"title":["On Fractional Fragility Rates of Graph Classes"],"prefix":"10.37236","volume":"27","author":[{"given":"Zden\u011bk","family":"Dvo\u0159\u00e1k","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-S\u00e9bastien","family":"Sereni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2020,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p9\/8190","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p9\/8190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,21]],"date-time":"2020-10-21T04:05:38Z","timestamp":1603253138000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/8909","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,16]]},"article-number":"P4.9"}}