Properly Colored Notions of Connectivity - A Dynamic Survey

Authors

Xueliang Li, Nankai University, ChinaFollow
Colton Magnant, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2015

Publication Title

Theory and Applications of Graphs

DOI

10.20429/tag.2015.000102

ISSN

2470-9859

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.

Comments

Creative Commons License

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

Recommended Citation

Li, Xueliang, Colton Magnant. 2015. "Properly Colored Notions of Connectivity - A Dynamic Survey." Theory and Applications of Graphs (1): Georgia Southern University Press. doi: 10.20429/tag.2015.000102
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/754