Chords in a Longest Cycle of a 3-Connected Graph

Abstract

In 1976, Carsten Thomassen conjectured that no longest cycle in a 3-connected graph can be a chordless cycle. Although this conjecture was later proved for some special classes of graphs, the general case remains open. In this work, we study how Thomason’s Lollipop Method was used by Thomassen to verify this conjecture for cubic graphs.