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1. THE EXTREMAL NUMBER OF THE SUBDIVISIONS OF THE COMPLETE BIPARTITE GRAPH.

Author

JANZER, OLIVER

Subjects
*BIPARTITE graphs, *COMPLETE graphs, *SUBDIVISION surfaces (Geometry), *EXTREMAL problems (Mathematics), *LOGICAL prediction
Abstract

For a graph F, the k-subdivision of F, denoted Fk, is the graph obtained by replacing the edges of F with internally vertex-disjoint paths of length k. In this paper, we prove that ex(n,Kk s,t) = O(n1+ s 1 sk), which is tight for t sufficiently large. This settles a conjecture of Conlon-- Janzer--Lee, and improves on a substantial body of work by Conlon--Janzer--Lee and Jiang--Qiu. [ABSTRACT FROM AUTHOR]

Published
2020
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