{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:03:18Z","timestamp":1770980598314,"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>Let $G$ be a connected graph with the usual shortest-path metric $d$. The graph $G$ is $\\delta$-hyperbolic provided for any vertices $x,y,u,v$ in it, the two larger of the three sums $d(u,v)+d(x,y),d(u,x)+d(v,y)$ and $d(u,y)+d(v,x)$ differ by at most $2\\delta.$ The graph $G$ is $k$-chordal provided it has no induced cycle of length greater than $k.$ Brinkmann, Koolen and Moulton find that every $3$-chordal graph is $1$-hyperbolic and that graph is not $\\frac{1}{2}$-hyperbolic if and only if it contains one of two special graphs as an isometric subgraph. For every $k\\geq 4,$ we show that a $k$-chordal graph must be $\\frac{\\lfloor\\frac{k}{2}\\rfloor}{2}$-hyperbolic and there does exist a $k$-chordal graph which is not $\\frac{\\lfloor \\frac{k-2}{2}\\rfloor}{2}$-hyperbolic. Moreover, we prove that a $5$-chordal graph is $\\frac{1}{2}$-hyperbolic if and only if it does not contain any of a list of five special graphs as an isometric subgraph.<\/jats:p>","DOI":"10.37236\/530","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:53:17Z","timestamp":1578714797000},"source":"Crossref","is-referenced-by-count":55,"title":["Hyperbolicity and Chordality of a Graph"],"prefix":"10.37236","volume":"18","author":[{"given":"Yaokun","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengpeng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,2,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p43\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:16:15Z","timestamp":1579302975000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/530","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,21]]},"article-number":"P43"}}