Document Type
Lecture
Publication Date
4-29-2005
Abstract
Thomassen [J. Graph Theory, 10 (1986) 309-324] conjectured that every 4-connected line graph is hamiltonian. Zhan in [Discrete Math., 89 (1991) 89-95] proved that every 7-connected line graph is hamiltonian connected. In this paper, we prove that every 3-edge-connected graph G has a cycle (edgedisjoint union of circuits) C with the property that for every cocircuit D of G with |D| ≥ 6, C ∩D= ∅. Consequently, every 6-connected line graph is hamiltonian.
Relational Format
presentation
Recommended Citation
Lai, Hongjian, "Every 6-connected line graph is hamiltonian" (2005). Combinatorics Seminar. 92.
https://egrove.olemiss.edu/math_combinatorics/92
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