平面图的圈基内插性质

The Cycle Basis Interpolation Property of Planar Graphs

图Ｇ的一个圈基的长度是该自基中所有圈的长度之和．设Ｃ－、Ｃ－分别是Ｇ的最小、最大圈基长度．如果对任一自然数Ｃ，Ｃ－＜Ｃ＜Ｃ－，都存在Ｇ的一个长为Ｃ的圈基，则称Ｇ有圈基内插性质．本文证明了无三角形的外平面图没有圈基内插性质，并说明存在围长任意大且有圈基内插性质的平面图．

The length of a cycle basis of a graph C is the sum of the lengths of its cycles. Let C,C- be the lengths of the minimal and maximal cycle basis. respectively. G has the cyCle basis interpolation property if for any integer C, C-<C<C-, there exists a cycle basis of G with length C. This paper proves that outer planar graphs without triangle have not cycle basis interpolation property. and shows that there are planar graphs with girth arbitrarily large having the cycle basis interpolation property.