Extending Paths and Degree Sums in Graphs
Chunfang Liu, Wang Jiang-lu · Advances in Mathematics · 2012
In this paper,we study the relations between degree sums and extending paths in graphs.The following result is proved.Let G be a graph of order n.If d(u) + d(v)≥n +(?)(n≤k≤n - 2) for each pair of nonadjacent vertices u,v in V(G),then every path P of G with k + 1≤\P n is extendable.The lower bound of |P| is sharp.