Bipancyclic subgraphs in random bipartite graphs [article]

Yilun Shang
2012 arXiv   pre-print
A bipartite graph on 2n vertices is bipancyclic if it contains cycles of all even lengths from 4 to 2n. In this paper we prove that the random bipartite graph G(n,n,p) with p(n)≫ n^-2/3 asymptotically almost surely has the following resilience property: Every Hamiltonian subgraph G' of G(n,n,p) with more than (1/2+o(1))n^2p edges is bipancyclic. This result is tight in two ways. First, the range of p is essentially best possible. Second, the proportion 1/2 of edges cannot be reduced. Our result
more » ... extends a classical theorem of Mitchem and Schmeichel.
arXiv:1211.6766v2 fatcat:tqd4szf5pzefdmql43tuvfdr6e