完全偶图的圈基内插性质

The Cycle Basis Interpolation Property of the Complete Bipartite Graph

图G的一个圈基的长度是该圈基的所有圈的长度之和 .设C-、C+ 分别是G的最小、最大圈基长度 ,如果对任一偶数C ,C-<C <C+ ,都存在G的一个长为C的圈基 ,则称G具有偶圈基内插性质 ,本文证明了 ,完全偶图Km ,n 具有偶圈基内插性质 .

The length of a cycle basis of a graph G is the sum of the lengths of its cycles. Let c -、c + be the minimum and maximum length of cycle basis of G respectively. Then G has the even cycle basis interpolation property(even cbip)if for any even integer c, c -<c<c +, there exists a cycle basis with length c. In this paper we prove that complete bipartite graph K m,n has the even cbip.