外可平面图的几乎唯一泛圈性

Almost Uniquely Pancyclic Quality of Outplannar Graphs

设G是阶为n的简单Hamilton图,若存在m(3≤m<n)使对每个l∈{3,4,…,n}-{m},G恰有一个长为l的圈且不含长为m的圈,则称G是几乎唯一泛圈图.用■k(i)表示具有n+k条边且满足一定条件的简单外可平面的H图的集合.文章讨论了■k(3)中图的几乎唯一泛圈性.

Let G be a simple Hamilton graph with n vertices. If there exists m （3≤m〈n） such that G contains exactly one cycle of length 1 for every ∫∈{3, 4, ..., n}-（m） and contains no cycle of length m, then G is called almost uniquely pancyclic graph. Let （i）/Гk denote the set of simple outplanar Hamilton graphs with n＋k edges and satisfy some certain conditions. In this paper we discuss the graphs in （3）/Гk in its almost uniquely pancyclic quality.