摘要
A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f(k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A fc-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f(k;h-1,h)<f(k,h), k≥3, h≥4.
A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f(k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A fc-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f(k;h-1,h)<f(k,h), k≥3, h≥4.
作者
Bao-guang Xu, Ping Wang, Jian-fang WangInstitute of Policy and Management, Chinese Academy of Sciences, Beijing 100080, ChinaDepartment of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS, Canada, B2G 2W5Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China
基金
the National Natural Science Foundation of China.
