{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:36:05Z","timestamp":1765546565449,"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>Let $2 \\leq k_1 &lt; k_2 &lt; \\ldots &lt; k_t $, $3 \\leq g_1 &lt; g_2 &lt; \\ldots &lt; g_s &lt; N$ be integer parameters. A $(k_1,k_2,\\ldots,k_t;g_1,g_2,\\dots,g_s;N)$-graph is a graph\u00a0that contains vertices of degrees $k_1,k_2,\\ldots,k_t$ but no other degrees and cycles of lengths $g_1,g_2,\\dots,g_s$ but no other cycles of length $&lt; N$.\u00a0For any given set of parameters satisfying the above conditions,\u00a0we present an explicit construction of $(k_1,k_2,\\ldots,k_t;g_1,g_2,\\dots,g_s;N)$-graphs and extend the concept of a cage (a smallest graph of given degree and girth) to that of a generalized cage -- a smallest\u00a0$(k_1,k_2,\\ldots,k_t;g_1,g_2,\\dots,g_s;N)$-graph. We introduce several infinite\u00a0families of generalized cages and study their basic properties\u00a0in the context of connected, bipartite, and vertex-transitive graphs, \u00a0as well as combinatorial configurations (in the context of multilaterals).<\/jats:p>","DOI":"10.37236\/4680","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:27:31Z","timestamp":1578702451000},"source":"Crossref","is-referenced-by-count":7,"title":["Generalized Cages"],"prefix":"10.37236","volume":"22","author":[{"given":"Marko","family":"Boben","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Jajcay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomaz","family":"Pisanski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,3,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p77\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p77\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:23:32Z","timestamp":1579256612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4680","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,3,23]]},"article-number":"P1.77"}}