Abstract
AbstractFor a bipartite graph , let be the largest such that either contains , a complete bipartite subgraph with parts of size , or the bipartite complement of contains as a subgraph. For a class of graphs , let . We say that a bipartite graph is strongly acyclic if neither nor its bipartite complement contains a cycle. By we denote the set of bipartite graphs with parts of size , which do not contain as an induced bipartite subgraph respecting the sides. One can easily show that for a positive if is not strongly acyclic. Here we ask whether is linear in for any strongly acyclic graph . We answer this question in the positive for all but four strongly acyclic graphs. We do not address this question for the remaining four graphs in this paper.
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