The bipartite-forbidden-graph conjecture for accumulation points

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For positive integers ss and tt, let Ks,tK_{s,t} be the complete bipartite graph with parts of sizes ss and tt, and let Forb⁡(Ks,t)\operatorname{Forb}(K_{s,t}) denote the hereditary property of graphs with no induced forbidden member Ks,tK_{s,t}. An accumulation point is a limit point of the edit distance function. Bipartite-forbidden-graph conjecture. For any s,t∈Ns,t\in\mathbb{N}, Forb⁡(Ks,t)\operatorname{Forb}(K_{s,t}) has no accumulation points in (0,1](0,1]. This extends the known result for the case treated earlier in the paper; the source notes that the conjecture requires methods beyond the existing argument, although it establishes absence of accumulation points on [1/2,1][1/2,1].

References

Primary source

Christopher Cox, Ryan R. Martin and Daniel McGinnis, “Accumulation points of the edit distance function”, arXiv:2107.06706 (2022).

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