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

DOI10.1002/jgt.22799zbMath1522.05054arXiv2005.09447OpenAlexW4210563818MaRDI QIDQ6081879

Pierre Aboulker, Martin Matamala, José Zamora, Laurent Beaudou

Publication date: 5 October 2023

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.09447

zbMATH Keywords

metric spaceslines in graphsChen-Chvatal conjecture

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Other designs, configurations (05B30) Structural characterization of families of graphs (05C75) Planar arrangements of lines and pseudolines (aspects of discrete geometry) (52C30) Other finite incidence structures (geometric aspects) (51E30)

Cites Work

• Lines, betweenness and metric spaces
• The Chen-Chvátal conjecture for metric spaces induced by distance-hereditary graphs
• Problems related to a de Bruijn-Erdös theorem
• Personal reminiscences and remarks on the mathematical work of Tibor Gallai
• Towards a de Bruijn-Erdős theorem in the \(L_1\)-metric
• A de Bruijn-Erdős theorem for chordal graphs
• A de Bruijn-Erdős theorem in graphs?
• A de Bruijn-Erdős theorem for 1–2 metric spaces
• A New Class of Graphs That Satisfies the Chen‐Chvátal Conjecture
• A de Bruijn - Erd\H{o}s theorem and metric spaces
• Lines in bipartite graphs and in 2‐metric spaces