Orientable quadrangulation of graphs (Q2757130)

This note shows a counteraxample to the denial of the conjecture that a \(d\)-regular bipartite graph of order \(2n\) has a quadrangulation if, and only if, \(nd\equiv 0\pmod 4\). Here, each face of a quadrangulation is restricted to a \(4\)-gon, i.e., a circuit of \(4\) edges. The conjecture was posed by \textit{T. Pisanski} [J. Graph Theory 4, 31-42 (1980; Zbl 0432.05024)[. The method used here is based on \textit{Y. Huang} and \textit{Y. Liu} [Sci. China, Ser. A 41, 498-504 (1998; Zbl 0946.05035)].