On the size of spheres of relations with a transitive group of automorphisms
نویسنده
چکیده
Let Γ = (V,E) be a point-transitive reflexive relation. Let v ∈ V and put r = |Γ(v)|. Also assume Γ(v) ∩ Γ−(v) = {v}. Then |Γ(v) \ Γ(v)| ≥ r − 1. In particular we have |Γ(v)| ≥ 1 + (r − 1)j. The last result confirms a recent conjecture of Seymour in the case vertex-transitive graphs. Also it gives a short proof for the validity of the Caccetta-Häggkvist conjecture for vertex-transitive graphs and generalizes an additive result of Shepherdson.
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تاریخ انتشار 2008