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Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs

Axenovich, Maria; Tompkins, Casey; Weber, Lea


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.

Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator KITopen-ID: 1000126051
Nachgewiesen in arXiv
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