{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830749,"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>We improve the best known bounds on average degree of online $k$-list-critical graphs for $k \\geqslant 6$. Specifically, for $k \\geqslant 7$ we show that every non-complete online $k$-list-critical graph has average degree at least $k-1 + \\frac{(k-3)^2 (2 k-3)}{k^4-2 k^3-11 k^2+28 k-14}$\u00a0and every non-complete online $6$-list-critical graph has average degree at least $5 + \\frac{93}{766}$.\u00a0The same bounds hold for offline $k$-list-critical graphs.<\/jats:p>","DOI":"10.37236\/6405","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:25Z","timestamp":1578670645000},"source":"Crossref","is-referenced-by-count":0,"title":["A Better Lower Bound on Average Degree of Online $k$-List-Critical Graphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Landon","family":"Rabern","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:38:08Z","timestamp":1579235888000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6405","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,2]]},"article-number":"P1.51"}}