New improvements on connectivity of cages
نویسندگان
چکیده
A (δ, g)-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all (δ, g)-cages with odd girth g ≥ 9 are r-connected, where (r − 1) ≤ δ + √ δ − 2 < r and all (δ, g)-cages with even girth g ≥ 10 are r-connected, where r is the largest integer satisfying r(r−1) 2 4 + 1 + 2r(r − 1) ≤ δ. Those results support a conjecture of Fu, Huang and Rodger that all (δ, g)-cages are δ-connected.
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