Upper bounds on the extremal number of the 4-cycle

FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) 0102 computer and information sciences 01 natural sciences
DOI: 10.48550/arxiv.2107.11601 Publication Date: 2023-02-17
ABSTRACT
AbstractWe obtain some new upper bounds on the maximum number of edges in ‐vertex graphs without containing cycles of length four. This leads to an asymptotically optimal bound on for a broad range of integers as well as a disproof of a conjecture of Erdős from 1970s which asserts that .
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