Longest cycles in certain bipartite graphs
For a connected bipartite graph with bipartition \((X,Y)\), where \(|X|= n \geq m = |Y|\geq 2\), the condition ``dist\((x,y) = 3\), \(x \in X\), \(y \in Y\) implies \(d(x) + d(y) \geq n+1\)'' ensures that a cycle of length \(2m\) exists. The graph is Hamiltonian if \(m=n\).
scientific article; zbMATH DE number 1127747