Long cycles in fullerene graphs
D. Kr\'al', O. Pangr\'ac, J.-S. Sereni, R. Skrekovski
TL;DR
This paper improves the known lower bound on the length of cycles in fullerene graphs, advancing the understanding of their Hamiltonian properties.
Contribution
It provides a tighter lower bound of 5n/6 - 2/3 for cycle lengths in fullerene graphs, refining previous results.
Findings
Cycle length bound improved from 4n/5 to 5n/6 - 2/3
Enhanced understanding of fullerene graph structure
Progress towards proving Hamiltonicity conjecture
Abstract
It is conjectured that every fullerene graph is hamiltonian. Jendrol' and Owens proved [J. Math. Chem. 18 (1995), pp. 83--90] that every fullerene graph on n vertices has a cycle of length at least 4n/5. In this paper, we improve this bound to 5n/6-2/3.
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