{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:40Z","timestamp":1753893820700,"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>For $r \\ge 2$, let $X$ be the number of $r$-armed stars $K_{1,r}$ in the binomial random graph $G_{n,p}$. \u00a0We study the upper tail ${\\mathbb P}(X \\ge (1+\\epsilon){\\mathbb E} X)$, and establish exponential bounds which are best possible up to constant factors in the exponent (for the special case of stars $K_{1,r}$ this solves a problem of Janson and Ruci\u0144ski, and confirms a conjecture by DeMarco and Kahn).\u00a0 In contrast to the widely accepted standard for the upper tail problem, we do not restrict our attention to constant $\\epsilon$, but also allow for $\\epsilon \\ge n^{-\\alpha}$ deviations.<\/jats:p>","DOI":"10.37236\/8493","type":"journal-article","created":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:44:42Z","timestamp":1584578682000},"source":"Crossref","is-referenced-by-count":7,"title":["Upper Tail Bounds for Stars"],"prefix":"10.37236","volume":"27","author":[{"given":"Matas","family":"\u0160ileikis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lutz","family":"Warnke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,3,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p67\/8057","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p67\/8057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:44:42Z","timestamp":1584578682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8493","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,3,12]]},"article-number":"P1.67"}}