{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852939,"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>The guessing game introduced by Riis [Electron. J. Combin. 2007] is a variant of the \"guessing your own hats\" game and can be played on any simple directed graph $G$ on $n$ vertices. For each digraph $G$, it is proved that there exists a unique guessing number $\\mathrm{gn}(G)$ associated to the guessing game played on $G$. When we consider the directed edge to be bidirected, in other words, the graph $G$ is undirected, Christofides and Markstr\u00f6m\u00a0[Electron. J. Combin. 2011] introduced a method to bound the value of the guessing number from below using the fractional clique cover number $\\kappa_f(G)$. In particular they showed $\\mathrm{gn}(G) \\geq |V(G)| - \\kappa_f(G)$. Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph \u00a0$G$ falls into one of the following categories: perfect graphs, cycle graphs or their complement. In this paper, we show that there are triangle-free graphs that have guessing numbers which do not meet the fractional clique cover bound. In particular, the famous triangle-free Higman-Sims graph has guessing number at least $77$ and at most $78$, while the bound given by fractional clique cover is $50$.<\/jats:p>","DOI":"10.37236\/4731","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:39:18Z","timestamp":1578692358000},"source":"Crossref","is-referenced-by-count":6,"title":["Guessing Games on Triangle-Free Graphs"],"prefix":"10.37236","volume":"23","author":[{"given":"Peter J.","family":"Cameron","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anh N.","family":"Dang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00f8ren","family":"Riis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2016,3,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p48\/data","content-type":"application\/zip","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:31:12Z","timestamp":1579239072000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/4731","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,3,18]]},"article-number":"P1.48"}}