{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:03Z","timestamp":1753893843957,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree $\\Delta$ and diameter $k$. For fixed $k$, the answer is $\\Theta(\\Delta^k)$. We consider the degree-diameter problem for particular classes of sparse graphs, and establish the following results. For graphs of bounded average degree the answer is $\\Theta(\\Delta^{k-1})$, and for graphs of bounded arboricity the answer is $\\Theta(\\Delta^{\\lfloor k\/2\\rfloor})$, in both cases for fixed $k$. For graphs of given treewidth, we determine the maximum number of vertices up to a constant factor. Other precise bounds are given for graphs embeddable on a given surface and apex-minor-free graphs.<\/jats:p>","DOI":"10.37236\/4313","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T18:46:08Z","timestamp":1578681968000},"source":"Crossref","is-referenced-by-count":1,"title":["The Degree-Diameter Problem for Sparse Graph Classes"],"prefix":"10.37236","volume":"22","author":[{"given":"Guillermo","family":"Pineda-Villavicencio","sequence":"first","affiliation":[]},{"given":"David R.","family":"Wood","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,6,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:15:52Z","timestamp":1579238152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4313","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,6,15]]},"article-number":"P2.46"}}