Ore and Erdős type conditions for long cycles in balanced bipartite graphs
Janusz Adamus (1) (2), Lech Adamus (3) (4)
(1) Department of Mathematics [London, Ontario]
(2) Institute of Mathematics [Krakow]
(3) Laboratoire de Recherche en Informatique
(4) Faculty of Applied Mathematics [Krakow]
Abstract
We conjecture Ore and Erdős type criteria for a balanced bipartite graph of order 2n to contain a long cycle C(2n-2k), where 0 <= k < n/2. For k = 0, these are the classical hamiltonicity criteria of Moon and Moser. The main two results of the paper assert that our conjectures hold for k = 1 as well.
