Cayley graph

Ramsey properties of Cayley graphs ★★★

Author(s): Alon

Conjecture   There exists a fixed constant $ c $ so that every abelian group $ G $ has a subset $ S \subseteq G $ with $ -S = S $ so that the Cayley graph $ {\mathit Cayley}(G,S) $ has no clique or independent set of size $ > c \log |G| $.

Keywords: Cayley graph; Ramsey number

Cores of Cayley graphs ★★

Author(s): Samal

Conjecture   Let $ M $ be an abelian group. Is the core of a Cayley graph (on some power of $ M $) a Cayley graph (on some power of $ M $)?

Keywords: Cayley graph; core

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