Second Hamiltonian Cycles in Claw-Free Graphs

Authors

Hossein EsfandiariFollow
Colton Magnant, Georgia Southern UniversityFollow
Pouria Salehi NowbandeganiFollow
Shirdareh HaghighiFollow

Publication Date

2015

Abstract

Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Esfandiari, Hossein; Magnant, Colton; Salehi Nowbandegani, Pouria; and Haghighi, Shirdareh (2015) "Second Hamiltonian Cycles in Claw-Free Graphs," Theory and Applications of Graphs: Vol. 2: Iss. 1, Article 2.
DOI: 10.20429/tag.2015.020102
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol2/iss1/2