度和与边数条件下过线性森林圈的一些研究

Researches on the Cycles through Linear Forest under the Conditions of Degree Sum and Edge Number

摘要: 2009年，Faudree提出在给定的σ₂(G)条件下，图G过(k,t)-线性森林的(k,t,2t+k)-泛圈问题。本文证明了在该σ₂(G)条件下，对任意，G中存在长为r或r+1的圈过(k,t)-线性森林。此外，本文还给出了图G是(k,t)-哈密顿的一个边数条件。

Abstract: In 2009, Faudree proposed the (k,t,2t+k) -pancyclic problem of graph G passing through (k,t) - linear forest under given σ₂(G) condition. In this paper, we prove that under the σ₂(G) condi-tion, for any , there exists a cycle passing through (k,t) -linear forest of length r or r+1 in the graph G. In addition, an edge number condition that graph G is (k,t)-Hamiltonian is given.