The longest paths(Cycles) in [5,3]-graphs
Wang Jiang-lu · Journal of Shandong University of Technology · 2006
A graph G is called[s,t]-graph,if there are at least t edges in every included subgraphs of s vertices.In this paper,we show the following results:(1)If G is a connected [5,3]-graph and |G|≥6,then the longest path of G is of length at least n-2.Moreover,n-2 is the best possible;(2) If G is a connected [5,3]-graph and |G|≥6,then the longest cycle of G is indefinte.