{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T17:49:36Z","timestamp":1763056176509,"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>The aim of this paper is to construct new small regular graphs with girth $7$ using integer programming techniques. Over the last two decades solvers for integer programs have become more and more powerful and have proven to be a useful aid for many hard combinatorial problems. Despite successes in many related fields, these optimisation tools have so far been absent in the quest for small regular graphs with a given girth. Here we illustrate the power of these solvers as an aid to construct small regular girth $7$ graphs from girth $8$ cages.<\/jats:p>","DOI":"10.37236\/4854","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T17:33:26Z","timestamp":1578677606000},"source":"Crossref","is-referenced-by-count":4,"title":["Applications of Integer Programming Methods to Cages"],"prefix":"10.37236","volume":"22","author":[{"given":"Frans J.C.T.","family":"De Ruiter","sequence":"first","affiliation":[]},{"given":"Norman L.","family":"Biggs","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,11,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:08:00Z","timestamp":1579237680000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,27]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/4854","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,11,27]]},"article-number":"P4.35"}}