New sufficient conditions for bipancyclic bipartite graphs

AbstractWe give here two sufficient conditions for a bipartite balanced graph of order 2n to be bipancyclic. The first one concerns graphs that satisfy a “bipartite Ore's condition”, that is graphs such that any two nonadjacent vertices in both parts of the bipartition have degree sum at least n, and the second one is for bipartite balanced traceable graphs containing an hamiltonian path whose extremities are nonadjacent and have degree sum at least n+1