dc.contributor.author | Cameron, PJ | en_US |
dc.contributor.author | Dang, AN | en_US |
dc.contributor.author | Riis, S | en_US |
dc.date.accessioned | 2016-02-05T11:37:35Z | |
dc.date.accessioned | 2016-04-18T10:26:56Z | |
dc.date.submitted | 2016-04-05T22:29:13.208Z | |
dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/11893 | |
dc.description | 9 pages, submitted to Electronic Journal of Combinatoric | |
dc.description | 9 pages, submitted to Electronic Journal of Combinatoric | en_US |
dc.description.abstract | The 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 Markstr om introduced a method to bound the value of the guessing number from below using the fractional clique number Kf(G). In particular they showed gn(G) >= |V(G)| - Kf(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. | en_US |
dc.language.iso | en | en_US |
dc.relation.replaces | http://qmro.qmul.ac.uk/xmlui/handle/123456789/11050 | |
dc.relation.replaces | 123456789/11050 | |
dc.rights | Original article available on arXiv; http://arxiv.org/abs/1410.2405, to be published in http://www.combinatorics.org/ | |
dc.subject | math.CO | en_US |
dc.subject | math.CO | en_US |
dc.subject | cs.IT | en_US |
dc.subject | math.IT | en_US |
dc.title | Guessing Games on Triangle-free Graphs | en_US |
dc.type | Article | |
pubs.author-url | http://arxiv.org/abs/1410.2405v2 | en_US |
pubs.notes | Not known | en_US |