{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T02:48:41Z","timestamp":1768877321372,"version":"3.49.0"},"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>Let $G$ be a graph on $n$ vertices with spectral radius $\\lambda$ (this is the largest eigenvalue of the adjacency matrix of $G$). We show that if $G$ does not contain the complete bipartite graph $K_{t ,s}$ as a subgraph, where $2\\le t \\le s$, then  $$\\lambda \\le \\Big((s-1)^{1\/t }+o(1)\\Big)n^{1-1\/t }$$ for fixed $t$ and $s$ while $n\\to\\infty$. Asymptotically, this bound matches the K\u0151v\u00e1ri-Tur\u00e1n-S\u00f3s upper bound on the average degree of $G$ (the Zarankiewicz problem). <\/jats:p>","DOI":"10.37236\/212","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:24:44Z","timestamp":1578698684000},"source":"Crossref","is-referenced-by-count":27,"title":["Spectral Extrema for Graphs: The Zarankiewicz Problem"],"prefix":"10.37236","volume":"16","author":[{"given":"L\u00e1szl\u00f3","family":"Babai","sequence":"first","affiliation":[]},{"given":"Barry","family":"Guiduli","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,9,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r123\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r123\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:40:27Z","timestamp":1579297227000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/212","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9,25]]},"article-number":"R123"}}