Longest cycles and their chords

1987/12/01 by Cun‐Quan Zhang · 2 citations

paper · doi:10.1002/jgt.3190110409

Abstract

Abstract Thomassen conjectured that any longest cycle of a 3‐connected graph has a chord. In this paper, we will show that the conjecture is true for a planar graph if it is cubic or δ ⩾ 4.

Cited by

• Chords of longest cycles in graphs with large circumferences
• Proof of a conjecture of Voss on bridges of longest cycles

Related

• Chords of longest cycles in graphs with large circumferences
• A conjecture implying Thomassen's chord conjecture in graph theory
• Chords of longest cycles passing through a specified small set
• Every longest circuit of a 3‐connected, K 3,3 ‐minor free graph has a chord
• Chords of longest circuits of graphs embedded in torus and Klein bottle