一类亚几乎唯一泛圈图

A Class of Sub-almost Uniquely Pancyclic Graphs

设G是阶为n的简单Hamilton图,若存在不同的p,q(3≤p<n,3≤q<n)使对每个l∈{3,4…,n}-{p,q},恰有一个长为l的圈且不含长为p,q的圈,则称G为亚几乎唯一泛圈图。用Γk表示具有n+k条边恰有12(k+1)(k+2)个圈的阶为n的简单Hamilton图的集合。本文确定了Γk中的所有亚几乎唯一泛圈图。并证明这些图除了一个5圈外都是简单MCD图。

Let G be a simple Hamilton graph with n vertices,If there exists p,q such that G contains exactly one cycle of length for every and contains no cycle of length of p,q.then G is called sub-almost uniquely pancyclic graph.Let denote the set of simple Hamilton graphs with n+k edges and cycles,In this paper all sub-almost uniquely pancyclic graphs in are determined and it is proved that they are all simple MCD graphs except 5 cycle.