Abstract
IfY is a finite graph then it is known that every sufficiently large groupG has a Cayley graph containing an induced subgraph isomorphic toY. This raises the question as to what is “sufficiently large”. Babai and Sós have used a probabilistic argument to show that |G| > 9.5 |Y|3 suffices. Using a form of greedy algorithm we strengthen this to\(|G| > (2 + \sqrt 3 )|Y|^3 \). Some related results on finite and infinite groups are included.
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References
Babai, L.: Embedding graphs in Cayley graphs. In: Probl. Comb. Théorie des Graphes (Proc. Conf. Paris-Orsay 1976) edited by J-C. Bermond, et al., pp. 13–15. Paris: C.N.R.S. 1976.
Babai, L., Sós, V.T.: Sidon sets in groups and induced subgraphs of Cayley graphs. Europ. J. Comb. (to appear)
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Godsil, C.D., Imrich, W. Embedding graphs in Cayley graphs. Graphs and Combinatorics 3, 39–43 (1987). https://doi.org/10.1007/BF01788527
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DOI: https://doi.org/10.1007/BF01788527