Abstract
A graphic sequence π = (d1, d2, …, dn) is said to be forcibly k-edge-connected if every realization of π is k-edge-connected. In this paper, we obtain a new sufficient degree condition for π to be forcibly k-edge-connected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for π to be forcibly 2-edge-connected and a conjecture about a strongest monotone degree condition for π to be forcibly 3-edge-connected due to Bauer et al. (Networks, 54(2) (2009) 95–98), and also implies a strongest monotone degree condition for π to be forcibly 4-edge-connected.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bauer, D., Hakimi, S.L., Kahl, N., Schmeichel, E. Sufficient degree conditions for k-edge-connectedness of a graph. Networks, 54(2): 95–98 (2009)
Boesch, F. The strongest monotone degree condition for n-connectedness of a graph. J. Combin. Theory Ser. B, 16: 162–165 (1974)
Bondy, J.A. Properties of graphs with constraints on degrees. Studia Sci. Math. Hungar, 4: 473–475 (1969)
Chvátal, V. On Hamilton’s ideals. J. Combin. Theory Ser. B, 12: 163–168 (1972)
Acknowledgments
The authors would like to thank the referees for their helpful suggestions and comments.
Funding
This paper is supported by the Hainan Provincial Natural Science Foundation of China (No. 2019RC085) and by the National Natural Science Foundation of China (No. 11961019).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yin, Jh., Guo, Jy. A New Sufficient Degree Condition for a Graphic Sequence to Be Forcibly k-Edge-Connected. Acta Math. Appl. Sin. Engl. Ser. 38, 223–228 (2022). https://doi.org/10.1007/s10255-022-1057-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-022-1057-9