%0 Journal Article
%T A Weakly Pancyclic Theorem for Hamiltonian Non-Bipartite Graphs<br>Hamilton非二部图的弱泛圈性
%A HE Fangguo
%A HU Zhiquan
%A <br>何方国
%A 胡智全
%J 系统科学与数学
%D 2008
%I 
%X 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 graph with more than \lfloor {{\textstyle{{n^2 } \over 4}}}\rfloor- n + 5 edges is weakly pancyclic. Bollobas and Thomason(1999) proved that every non-bipartite graph of order n and size at least \lfloor{{{\textstyle{{n^2 } \over 4}}}\rfloor - n + 59 is weakly pancyclic. In this paper, the following result is established: let G be a Hamiltonian non-bipartite graph of order $n$ and size at least \lfloor {{\textstyle{{n^2 } \over 4}}}\rfloor - n + 12, then G is weakly pancyclic.
%K Non-bipartite graph
%K Hamiltonian graph cycle
%K weakly pancyclic graph<br>非二部图
%K Hamilton图
%K 圈
%K 弱泛圈图
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=08552210540C7462AE35FE3BE4E67A46&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=F3090AE9B60B7ED1&sid=55C36125E841856F&eid=4944E31C6DB9BAF5&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=11