{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:49Z","timestamp":1753893769167,"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>A set $M$ of edges of a graph $G$ is a matching if no two edges in $M$ are incident to the same vertex. The matching number of $G$ is the maximum cardinality of a matching of $G$. A set $S$ of vertices in $G$ is a total dominating  set of $G$ if every vertex of $G$ is adjacent to some vertex in $S$. The minimum cardinality of a total dominating set of $G$ is the total domination number of $G$. If $G$ does not contain $K_{1,3}$ as an induced subgraph, then $G$ is said to be claw-free. We observe that the total domination number of every claw-free graph with minimum degree at least three is bounded above by its matching number. In this paper, we use transversals in hypergraphs to characterize connected claw-free graphs with minimum degree at least three that have equal total domination and matching numbers.<\/jats:p>","DOI":"10.37236\/1085","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:59:32Z","timestamp":1578718772000},"source":"Crossref","is-referenced-by-count":20,"title":["Total Domination and Matching Numbers in Claw-Free Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Michael A.","family":"Henning","sequence":"first","affiliation":[]},{"given":"Anders","family":"Yeo","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:10:22Z","timestamp":1579320622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1085","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,7,28]]},"article-number":"R59"}}