{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:10Z","timestamp":1753893850125,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>\u00a0Let $G$ be a complete convex geometric graph whose vertex set $P$ forms a convex polygon $C$, and let $\\mathcal{F}$ be a family of subgraphs of $G$. A blocker\u00a0for $\\mathcal{F}$ is a set of diagonals of $C$, of smallest possible size, that contains a common edge with every element of $\\mathcal{F}$. Previous works determined the blockers for various families $\\mathcal{F}$ of non-crossing subgraphs, including the families of all perfect matchings, all spanning trees, all Hamiltonian paths, etc.\r\nIn this paper we present a complete characterization of the family $\\mathcal{B}$ of blockers for the family $\\mathcal{T}$ of triangulations\u00a0of $C$. In particular, we show that $|\\mathcal{B}|=F_{2n-8}$, where $F_k$ is the $k$'th element in the Fibonacci sequence and $n=|P|$.\r\nWe use our characterization to obtain a tight result on a geometric Maker-Breaker game in which the board is the set of diagonals\u00a0 of a convex $n$-gon $C$ and Maker seeks to occupy a triangulation of $C$. We show that in the $(1:1)$ triangulation game, Maker can ensure \u00a0a win within $n-3$ moves, and that in the $(1:2)$ triangulation game, Breaker can ensure a win within $n-3$ moves. In particular, the threshold bias for\u00a0the game is $2$.<\/jats:p>","DOI":"10.37236\/7205","type":"journal-article","created":{"date-parts":[[2020,10,21]],"date-time":"2020-10-21T04:05:53Z","timestamp":1603253153000},"source":"Crossref","is-referenced-by-count":0,"title":["Blockers for Triangulations of a Convex Polygon and a Geometric Maker-Breaker Game"],"prefix":"10.37236","volume":"27","author":[{"given":"Chaya","family":"Keller","sequence":"first","affiliation":[]},{"given":"Yael","family":"Stein","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p12\/8193","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p12\/8193","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,21]],"date-time":"2020-10-21T04:05:53Z","timestamp":1603253153000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/7205","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,10,16]]},"article-number":"P4.12"}}