At least half of the leapfrog fullerene graphs have exponentially many Hamilton cycles. Issue 3 (11th January 2021)

• Record Type: Journal Article
• Authors: Kardoš, František; Mockovčiaková, Martina
• Is Part Of: Journal of graph theory. Volume 97:Issue 3(2021)
• Page Start: 382
• Page End: 392
• Publication Date: 2021-01-11
• Subjects: fullerene graph -- Hamilton cycle; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22660
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: A fullerene graph is a 3‐connected cubic planar graph with pentagonal and hexagonal faces. The leapfrog transformation of a planar graph produces the dual of the truncation of the given graph. A fullerene graph is a leapfrog if it can be obtained from another fullerene graph by the leapfrog transformation. We prove that leapfrog fullerene graphs on n = 12 k − 6 vertices have at least 2 k Hamilton cycles.