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- W4386857982 abstract "The long standing Zarankiewicz's conjecture states that the crossing number cr(Km,n) of the complete bipartite graph is Z(m,n):= [m/2][m-1/2][n/2][n-1/2]. Using flag algebras we show that cr(Kn,n) ≥ 0.9118 • Z(n, n) + o(n4). We also show that the rectilinear crossing number cr-(Kn,n) of Kn,n is at least 0.987 • Z(n,n) + o(n4). Finally, we show that if a drawing of Kn,n has no K3,4 that has exactly two crossings, and these crossings share exactly one vertex, then it has at least Z(n,n) + o(n4) crossings. This is a local restriction inspired by Turán type problems that gives an asymptotically tight result." @default.
- W4386857982 created "2023-09-20" @default.
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- W4386857982 date "2023-01-01" @default.
- W4386857982 modified "2023-09-27" @default.
- W4386857982 title "Crossing numbers of complete bipartite graphs" @default.
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- W4386857982 doi "https://doi.org/10.1016/j.procs.2023.08.216" @default.
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