Given a bipartite graph G with m and n vertices, respectively,in its vertices classes, and given two integers s, t such that 2 ≤ s ≤ t, 0 ≤ m−s ≤ n−t, and m+n ≤ 2s+t−1, we prove that if G has at least mn−(2(m−s)+n−t) edges then it contains a subdivision of the complete bipartite $K_(s,t)$ with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn − (2(m − s) + n − t + 1) edges for this topological Turan type problem.
CitationBalbuena Martínez, Maria Camino Teófila [et al.]. Subdivisions in a bipartite graph. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 39-61.
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