Extendability of the complementary prism of bipartite graphs

For a nonnegative integer k, a connected graph G of order at least 2k+2 is k-extendable if G has a perfect matching and every set of k independent edges extends to a perfect matching in G. The largest integer k such that G is k-extendable is called the extendability of G. The complementary prism G (G) over bar of G is the graph constructed from G and its complement (G) over bar defined on a set of vertices disjoint from V (G) (i.e. V(G) boolean AND V((G) over bar) = O) by joining each pair of corresponding vertices by an edge. Janseana and Ananchuen [Thai J. Math. 13 (2015), 703-721] gave a lower bound to the extendability of G (G) over bar in terms of the extendabilities of G and (G) over bar in the case that neither G nor (G) over bar is a bipartite graph. In this paper, we consider the remaining case and give a sharp lower bound to the extendability of G (G) over bar when G is a bipartite graph.