{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:31:35Z","timestamp":1761611495770,"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>Every $n$-vertex graph has two vertices with the same degree (if $n\\ge2$).  In general, let rep$(G)$ be the maximum multiplicity of a vertex degree in $G$.  An easy counting argument yields rep$(G)\\ge n\/(2d-2s+1)$, where $d$ is the average degree and $s$ is the minimum degree of $G$.  Equality can hold when $2d$ is an integer, and the bound is approximately sharp in general, even when $G$ is restricted to be a tree, maximal outerplanar graph, planar triangulation, or claw-free graph.  Among large claw-free graphs, repetition number $2$ is achievable, but if $G$ is an $n$-vertex line graph, then rep$(G)\\ge{1\\over4}n^{1\/3}$.  Among line graphs of trees, the minimum repetition number is $\\Theta(n^{1\/2})$.  For line graphs of maximal outerplanar graphs, trees with perfect matchings, or triangulations with 2-factors, the lower bound is linear.<\/jats:p>","DOI":"10.37236\/96","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:36:45Z","timestamp":1578717405000},"source":"Crossref","is-referenced-by-count":6,"title":["Repetition Number of Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Yair","family":"Caro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douglas B.","family":"West","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:14:37Z","timestamp":1579317277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/96","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,1,7]]},"article-number":"R7"}}