Every longest circuit of a 3-connected, $K_{3,3}$-minor free graph has a chord

Details Every longest circuit of a 3-connected, $K_{3,3}$-minor free graph has a chord Every longest circuit of a 3-connected, $K_{3,3}$-minor free graph has a chord

2007-11-15

arxiv.org/abs/0711.2360v2

Journal of Graph Theory, 58 (4): 293-298, 2008

Mathematics

Combinatorics

accepted by Journal of Graph Theory

Scientific paper

10.1002/jgt.20312

Carsten Thomassen conjectured that every longest circuit in a 3-connected
graph has a chord. We prove the conjecture for graphs having no $K_{3,3}$
minor, and consequently for planar graphs.

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