{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T02:40:10Z","timestamp":1773974410071,"version":"3.50.1"},"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 a graph $T$ and a set of graphs $\\mathcal{H}$, let $\\mbox{ex}(n,T,\\mathcal{H})$ denote the maximum number of copies of $T$ in an $n$-vertex $\\mathcal{H}$-free graph. Recently, Alon and Frankl [Journal of Combinatorial Theory, Series B, 2024] determined the exact value of $\\mbox{ex}(n,K_2,\\{K_{k+1},M_{s+1}\\})$, where $K_{k+1}$ and $M_{s+1}$ are complete graph on $k+1$ vertices and matching of size $s+1$, respectively. In this paper, we continue the study of the function $\\mbox{ex}(n, T,\\{K_{k+1},M_{s+1}\\})$. We determine the exact value of $\\mbox{ex}(n,K_r,\\{K_{k+1},M_{s+1}\\})$ for $r\\ge 3$ and the exact value of $\\mbox{ex}(n,S_r,\\{K_{k+1},M_{s+1}\\})$ for $n\\ge 2(s+1)(r+1)$ and $r\\ge 2$.<\/jats:p>","DOI":"10.37236\/13563","type":"journal-article","created":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:22:08Z","timestamp":1773440528000},"source":"Crossref","is-referenced-by-count":1,"title":["Generalized Tur\u00e1n Problem with Bounded Matching Number"],"prefix":"10.37236","volume":"33","author":[{"given":"Yue","family":"Ma","sequence":"first","affiliation":[]},{"given":"Xinmin","family":"Hou","sequence":"additional","affiliation":[]},{"given":"Zhi","family":"Yin","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:22:15Z","timestamp":1773440535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/13563","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,13]]},"article-number":"P1.46"}}