A bipartite r-uniform hypergraph \(H=(X,Y,E)\) is said to be bi-k-edge-maximal if every subhypergraph \(H'\) of H has edge-connectivity at most k, but for any edge e in \(H^{bc}\) , \(H+e=(X,Y,E\cup \{e\})\) contains a subhypergraph with edge-connectivity at least \(k+1\) . Here, \(H^{bc}\) is the bipartite r-uniform hypergraph with bipartition (X, Y) and edge set \(E(H^{bc})\) \(=\{e\subseteq X\cup\) \(Y:~e\cap X\ne \emptyset ,\) \(~e\cap Y\ne \emptyset ,\) \(~e\notin E(H)\) \(~\text {and}~ e~\text {has cardinality}~ r\}\) . In this paper, we investigate the upper and lower bounds on the sizes of bi-k-edge-maximal r-uniform hypergraphs. Furthermore, some extremal hypergraphs achieving these bounds are characterized. This complements previous results on bi-k-edge-maximal graphs.
