{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:00Z","timestamp":1753893840237,"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>Riis [Electron. J. Combin., 14(1):R44, 2007] introduced a guessing game for graphs which is equivalent to finding protocols for network coding. In this paper we prove upper and lower bounds for the winning probability of the guessing game on undirected graphs.  We find optimal bounds for perfect graphs and minimally imperfect graphs, and present a conjecture relating the exact  value for all graphs to the fractional chromatic number.<\/jats:p>","DOI":"10.37236\/679","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:41:30Z","timestamp":1578714090000},"source":"Crossref","is-referenced-by-count":11,"title":["The Guessing Number of Undirected Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Demetres","family":"Christofides","sequence":"first","affiliation":[]},{"given":"Klas","family":"Markstr\u00f6m","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,9,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p192\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p192\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:01:26Z","timestamp":1579302086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p192"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/679","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,9,26]]},"article-number":"P192"}}