[{"type":"report","title":"Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs [in press]","issued":{"date-parts":[["2020"]]},"author":[{"family":"Axenovich","given":"Maria"},{"family":"Tompkins","given":"Casey"},{"family":"Weber","given":"Lea"}],"abstract":"For a bipartite graph G, let h(G) be the largest t such that either G or the bipartite complement of G contain K$_{t,t}$. For a class F of graphs, let h(F)= min {h(G): G\\in F}. We say that a bipartite graph H is strongly acyclic if neither H nor its bipartite complement contain a cycle. By Forb(n, H) we denote a set of bipartite graphs with parts of sizes n each, that do not contain H as an induced bipartite subgraph respecting the sides. One can easily show that h(Forb(n,H))= O(n$^{1-s}$) for a positive s if H is not strongly acyclic. Here, we prove that h(Forb(n, H)) is linear in n for all strongly acyclic graphs except for four graphs.","kit-publication-id":"1000126051"}]