A WEAKLY PANCYCLIC THEOREM FOR HAMILTONIAN NON-BIPARTITE GRAPHS
Fangguo He · Xitong kexue yu shuxue · 2008
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[(n~2)/4]-n + 5 edges is weakly pancyclic.Bollobas and Thomason(1999) proved that every non-bipartite graph of order n and size at least[(n~2)/4]-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[(n~2)/4]-n+12,then G is weakly pancyclic.