科研之友
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摘要
A (delta, g)-cage is a delta-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all (delta, g)-cages with odd girth g >= 9 are r-connected, where (r - 1)(2) <= delta + root delta - 2 < r (2) and all (delta, 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) <= delta. These results support a conjecture of Fu, Huang and Rodger that all (delta, g)-cages are delta-connected.
