2-biplacement without fixed points of (p,q)-bipartite graphs

Abstract

In this paper we consider 2-biplacement without fixed points of paths and $(p, q)$-bipartite graphs of small size. We give all $(p, q)$-bipartite graphs $G$ of size q for which the set $\mathcal{S}^{*}(G)$ of all 2-biplacements of $G$ without fixed points is empty.