A New Class of Graphs That Satisfies the Chen‐Chvátal Conjecture | Zendy

Aboulker P. | Zendy; Matamala M. | Zendy; Rochet P. | Zendy; Zamora J. | Zendy

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A New Class of Graphs That Satisfies the Chen‐Chvátal Conjecture

Author(s) -

Aboulker P.,

Matamala M.,

Rochet P.,

Zamora J.

Publication year - 2018

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22142

Subject(s) - combinatorics , mathematics , conjecture , chordal graph , chen , plane (geometry) , discrete mathematics , class (philosophy) , graph , computer science , paleontology , geometry , artificial intelligence , biology

A well‐known combinatorial theorem says that a set of n non‐collinear points in the plane determines at least n distinct lines. Chen and Chvátal conjectured that this theorem extends to metric spaces, with an appropriated definition of line. In this work, we prove a slightly stronger version of Chen and Chvátal conjecture for a family of graphs containing chordal graphs and distance‐hereditary graphs.

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