Graphs with no induced house nor induced hole have the de Bruijn–Erdös property

Pierre Aboulker, Laurent Beaudou, Martı́n Matamala, José Zamora

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

A set of (Formula presented.) points in the plane which are not all collinear defines at least (Formula presented.) distinct lines. Chen and Chvátal conjectured in 2008 that a similar result can be achieved in the broader context of finite metric spaces. This conjecture remains open even for graph metrics. In this article we prove that graphs with no induced house nor induced cycle of length at least 5 verify the desired property. We focus on lines generated by vertices at distance at most 2, define a new notion of 'good pairs' that might have application in larger families, and finally use a discharging technique to count lines in irreducible graphs.

Original languageEnglish
JournalJournal of Graph Theory
DOIs
Publication statusAccepted/In press - 2022

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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