Characterization of forcibly bipartite self-complementary bipartitioned sequences

Abstract

A bipartitioned graph is an ordered pair (G,P) where G is a bipartite graph and P={A,B} is a bipartition of G. The bipartite complement of (G,P) is the bipartitioned graph $(\bar G(P),P)$ where $\bar G(P)$ is the complement of G with respect to the complete bipartite graph $K_{\left| A \right|,\left| B \right|}$. If $G \simeq \bar G(P)$ then (G,P) is called bipartite self-complementary. In this paper we characterise all those bipartitioned sequences τ=(d₁,…,d_m⋎e₁,…,e_n) such that τ is graphic and all realisations of τ are bipartite self-complementary.