Theory and Applications of Graphs
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.
Li, Xueliang, Colton Magnant.
"Properly Colored Notions of Connectivity - A Dynamic Survey."
Theory and Applications of Graphs (1): Georgia Southern University Press.
doi: 10.20429/tag.2015.000102 source: https://digitalcommons.georgiasouthern.edu/tag/vol0/iss1/2/