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dc.contributor.authorCameron, Peter Jephson
dc.contributor.authorDang, Anh
dc.contributor.authorRiis, Soren
dc.identifier.citationCameron , P J , Dang , A & Riis , S 2016 , ' Guessing games on triangle-free graphs ' , Electronic Journal of Combinatorics , vol. 23 , no. 1 , P1.48 . < >en
dc.identifier.otherORCID: /0000-0003-3130-9505/work/58055583
dc.description.abstractThe guessing game introduced by Riis 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 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 Markström 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 gn(G) >= |V(G)| - kappa_f(G). Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph 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.
dc.relation.ispartofElectronic Journal of Combinatoricsen
dc.subjectNetwork codingen
dc.subjectGuessing numberen
dc.subjectClique cover numberen
dc.subjectHigman-Sims graphen
dc.subjectQA Mathematicsen
dc.titleGuessing games on triangle-free graphsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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