On 2-factors with prescribed properties in a bipartite graph (Q2508633)

A cycle of length 4 is called a quadrilateral. Recently \textit{J. Yan} and \textit{G. Liu} [J. Syst. Sci. Complex. 17, 532--537 (2004; Zbl 1080.05051)] investigated the minimum degree conditions sufficient for \(G\) to contain \(k\) vertex-disjoint quadrilaterals containing specified edges. In the same paper the authors conjectured that for any \(k\) independent edges \(e_1,e_2,\dots, e_k\) of a graph \(G\), \(G\) has a 2-factor with \(k\) cycles \(C_1,C_2,\dots, C_k\) such that \(e_i\) is on \(C_i\), \(1\leq i\leq k\), where \(k-1\) of the cycles are quadrilaterals. Here the authors prove this conjecture.