Bipartite embedding of (p,q)-trees

Abstract. A bipartite graph \(G=(L,R;E)\) where \(V(G)=L\cup R\), \(|L|=p\), \(|R| =q\) is called a \((p,q)\)-tree if \(|E(G)|=p+q-1\) and \(G\) has no cycles. A bipartite graph \(G=(L,R;E)\) is a subgraph of a bipartite graph \(H=(L',R';E')\) if \(L\subseteq L'\), \(R\subseteq R'\) and \(E\subseteq E'\). In this paper we present sufficient degree conditions for a bipartite graph to contain a \((p,q)\)-tree.