PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
February 8, 2026Journal of Combinatorial Designs0 citations

Combining the Theorems of Turán and de Bruijn–Erdős

View Full Paper
SCSayok ChakravartyDMDhruv Mubayi

Key Points

  • To generalize the de Bruijn–Erdős theorem by exploring conditions for points and lines in linear spaces.
  • Fixed an integer for analysis of point-line relationships
  • Defined a set of points and lines in a linear space
  • Considered conditions for pairs of points lying on lines
  • Proved results are sharp when the integer is a multiple of a specified value
  • Demonstrated that conditions hold for large integers
  • Results applicable in the context of linear hypergraphs

Abstract

ABSTRACT Fix an integer . Let be a set of points and let be a set of lines in a linear space such that no line in contains more than points of . Suppose that for every ‐set in , there is a pair of points in that lies in a line from . We prove that for large, and this is sharp when is a multiple of . This generalizes the de Bruijn–Erdős theorem, which is the case . Our result is proved in the more general setting of linear hypergraphs.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Chakravarty et al. (2026) studied this question.

synapsesocial.com/papers/698828010fc35cd7a88470dehttps://doi.org/10.1002/jcd.70008
Ask AI
Helpful
Bookmark
Share
View Full Paper