{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T20:45:19Z","timestamp":1769114719420,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a graph $G$ and a set $\\mathcal{F}$ of connected graphs, $G$ is said be $\\mathcal{F}$-free if $G$ does not contain any member of $\\mathcal{F}$ as an induced subgraph.\u00a0We let $\\mathcal{G} _{3}(\\mathcal{F})$ denote the set of all $3$-connected $\\mathcal{F}$-free graphs.\u00a0This paper is concerned with sets $\\mathcal{F}$ of connected graphs such that $|\\mathcal{F}|=3$ and $\\mathcal{G} _{3}(\\mathcal{F})$ is finite.\u00a0Among other results, we show that for an integer $m\\geq 3$ and a connected graph $T$ of order greater than or equal to $4$, $\\mathcal{G} _{3}(\\{K_{4},K_{2,m},T\\})$ is finite if and only if $T$ is a path of order $4$ or $5$.<\/jats:p>","DOI":"10.37236\/3255","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:29:00Z","timestamp":1578698940000},"source":"Crossref","is-referenced-by-count":4,"title":["Forbidden Triples Generating a Finite set of 3-Connected Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Yoshimi","family":"Egawa","sequence":"first","affiliation":[]},{"given":"Jun","family":"Fujisawa","sequence":"additional","affiliation":[]},{"given":"Michitaka","family":"Furuya","sequence":"additional","affiliation":[]},{"given":"Michael D","family":"Plummer","sequence":"additional","affiliation":[]},{"given":"Akira","family":"Saito","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,7,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:14:14Z","timestamp":1579256054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,17]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/3255","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,17]]},"article-number":"P3.13"}}