Abstract
Let Γ be a connected directed Cayley graph with outdegreer. We show that there is a cutset of size ≤ (4n In(n/2))/D whose deletion creates a sinkB and a sourceB such that ¦B¦ = ¦B¦. In particular Γ can be separated into two equal parts by deleting less than (8e/r)n (1-1/r) In(n/2) vertices. Our results improve a recent one proved by Annexstein and Baumslag [1]. As a main tool, we use inequalities from additive number theory.
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References
F. Annexstein, M. Baumslag, On the diameter and bisector size of Cayley graphs,Math. Systems Theory 26 (1993), 271–291.
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I. Z. Rusza, An application of Graph theory to additive number theory,Scientia Ser. A 3 (1989), 97–109.
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Hamidoune, Y.O., Serra, O. On small cuts separating an abelian Cayley graph into two equal parts. Math. Systems Theory 29, 407–409 (1996). https://doi.org/10.1007/BF01192695
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DOI: https://doi.org/10.1007/BF01192695