Hamilton非二部图的弱泛圈性

A WEAKLY PANCYCLIC THEOREM FOR HAMILTONIAN NON-BIPARTITE GRAPHS

图G称为弱泛圈图是指G包含了每个长为l(g(G)≤l≤c(G))的圈,其中g(G),c(G)分别是G的围长与周长.1997年Brandt提出以下猜想:边数大于[(n^2)/4]-n+5的n阶非二部图为弱泛圈图.1999年Bollobás和Thomason证明了边数不小于[(n^2)/4]-n+59的n阶非二部图为弱泛圈图.作者证明了如下结论:设G是n阶Hamilton非二部图,若G的边数不小于[(n^2)/4]-n+12,则G为弱泛圈图.

An n-vertex graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In 1977, Brandt conjectured that an n-vertex non-bipartite with more than [n^2/4]- n ＋5 edges is weakly pancyclic. Bollobas and Thomason（1999） graph of order n and size at least [n^2/4]- n＋59 is weakly proved that every non-bipartite graph pancyclic. In this paper, the following result is established： let G be a Hamiltonian non- and size at least [n^2/4]-n ＋ 12, then G is weakly paneyclic. bipartite graph of order