{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822844,"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>If $X$ is a geodesic metric space and $x_1,x_2,x_3\\in X$, a geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\\delta$-hyperbolic $($in the Gromov sense$)$ if any side of $T$ is contained in a $\\delta$-neighborhood of the union of the other two sides, for every geodesic triangle $T$ in $X$. We denote by $\\delta(X)$ the sharp hyperbolicity constant of $X$, i.e., $\\delta(X):=\\inf\\{\\delta\\ge 0: \\, X \\, \\text{ is $\\delta$-hyperbolic}\\,\\}$. The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. One of the main aims of this paper is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph $G\\setminus e$ obtained from the graph $G$ by deleting an arbitrary edge $e$ from it. These inequalities allow to obtain the other main result of this paper, which characterizes in a quantitative way the hyperbolicity of any graph in terms of local hyperbolicity. <\/jats:p>","DOI":"10.37236\/2175","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:30:29Z","timestamp":1578713429000},"source":"Crossref","is-referenced-by-count":9,"title":["Distortion of the Hyperbolicity Constant of a Graph"],"prefix":"10.37236","volume":"19","author":[{"given":"Walter","family":"Carballosa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Domingo","family":"Pestana","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M.","family":"Rodr\u00edguez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M.","family":"Sigarreta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p67\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:36:50Z","timestamp":1579300610000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/2175","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,3,31]]},"article-number":"P67"}}