Partition of a bipartite graph into cycles (Q686183)

Let \(n= n_ 1+ n_ 2+\cdots + n_ k\) with \(n_ 1\geq n_ 2\geq\cdots \geq n_ k\geq 2\), \(k\geq 2\). The paper shows that a bipartite graph \(G\) with bipartition \(V(G)= V_ 1\cup V_ 2\), \(| V_ 1|= | V_ 2|= n\) and minimum degree at least \(n_ 1+ n_ 2+ \cdots +{1\over 2} n_ k\), contains \(k\) vertex-disjoint cycles of lengths \(2n_ 1,2n_ 2,\dots,2n_ k\), respectively. The sharpness of the results is also established.