Progress on dirac's conjecture

Michael Stuart Payne, David Wood

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

In 1951, Gabriel Dirac conjectured that every non-collinear set P of n points in the plane contains a point incident to at least of the lines determined by P, for some constant c. The following weakened conjecture was proved by Beck and by Szemerédi and Trotter: every non-collinear set P of n points in the plane contains a point in at least lines determined by P, for some constant c0. We prove this result with We also give the best known constant for Beck's Theorem, proving that every set of n points with at most ' collinear determines at least lines.

Original languageEnglish
Number of pages9
JournalThe Electronic Journal of Combinatorics
Volume21
Issue number2
Publication statusPublished - 16 Apr 2014

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