摘要
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）2 ≤δ ＋ x/δ - 2 〈 r2 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. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.
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）2 ≤δ ＋ x/δ - 2 〈 r2 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. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.
