Thomassen's chord conjecture for longest cycles in 3-connected graphs
A graph is 3-connected if deleting fewer than three vertices leaves it connected. A chord of a cycle is an edge joining two nonconsecutive vertices of the cycle. Thomassen's chord conjecture. Every longest cycle in a -connected graph has a chord. This conjecture is a major unsolved problem in graph theory, although it has been proved for cubic graphs and several other classes of graphs.
References
Primary source
Chengli Li and Feng Liu, “Bound vertices of longest paths between two vertices in cubic graphs”, arXiv:2406.07942 (2025).
Additional references
2 papers in this index state this conjecture (2007–2024). The statement above is taken from the most recent of them; the others are arXiv:0711.2360.
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