{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T04:54:27Z","timestamp":1776401667569,"version":"3.51.2"},"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>Let $r$ and $m$ be two integers such that $r\\geq m$. Let $H$ be a graph with order $|H|$, size $e$ and maximum degree $r$ such that $2e\\geq |H|r-m$. We find a best lower bound  on spectral radius of graph $H$ in terms of $m$ and $r$. Let $G$ be a connected $r$-regular graph of order $|G|$ and $ k &lt; r$ be an integer. Using the previous results, we find some best upper bounds (in terms of $r$ and $k$) on the third largest eigenvalue that is sufficient to guarantee that $G$ has a $k$-factor when $k|G|$ is even. Moreover, we find a best bound on the second largest eigenvalue that is sufficient to guarantee that $G$ is $k$-critical when $k|G|$ is odd. Our results extend the work of Cioab\u0103,  Gregory and Haemers [J. Combin. Theory Ser. B, 1999] who obtained such results for 1-factors.<\/jats:p>","DOI":"10.37236\/431","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:59:11Z","timestamp":1578715151000},"source":"Crossref","is-referenced-by-count":13,"title":["Regular Factors of Regular Graphs from Eigenvalues"],"prefix":"10.37236","volume":"17","author":[{"given":"Hongliang","family":"Lu","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,11,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r159\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r159\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:21:44Z","timestamp":1579303304000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/431","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,26]]},"article-number":"R159"}}