Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs

Rao Li; Anuj Daga; Vivek Gupta; Manad Mishra; Spandan Kumar Sahu; Ayush Sinha

doi:10.33401/fujma.450809

Research Article

Year 2018, Volume: 1 Issue: 2, 191 - 193, 25.12.2018

Rao Li , Anuj Daga Vivek Gupta Manad Mishra Spandan Kumar Sahu Ayush Sinha

https://doi.org/10.33401/fujma.450809

Abstract

References

[1] Zh. G. Nikoghosyan, A size bound for Hamilton cycles, (2011), arXiv:1107.2201 [math.CO].
[2] J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, Macmillan, London and Elsevier, New York, 1976.
[3] Zh. G. Nikoghosyan, Two sufficient conditions for Hamilton and dominating cycles, Int. J. Math. Math. Sci., 2012 (2012), Article ID 185346, 25 pages, doi:10.1155/2012/185346.
[4] K. Zhao, Dirac type condition and Hamiltonian graphs, Serdica Math. J. 37 (2011), 277–282.
[5] D. W. Cranston, S. O, Hamiltonicity in connected regular graphs, Inform. Process. Lett., 113 (2013), 858–860.

Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs

Year 2018, Volume: 1 Issue: 2, 191 - 193, 25.12.2018

Rao Li , Anuj Daga Vivek Gupta Manad Mishra Spandan Kumar Sahu Ayush Sinha

https://doi.org/10.33401/fujma.450809

Abstract

A graph is called Hamiltonian (resp. traceable) if the graph has a Hamiltonian cycle (resp. path), a cycle (resp. path) containing all the vertices of the graph. In this note, we present sufficient conditions involving minimum degree and size for Hamiltonian and traceable graphs. One of the sufficient conditions strengthens the result obtained by Nikoghosyan in [1].

Keywords

Hamiltonian graph , Minimum degree , Traceable graph

References

[1] Zh. G. Nikoghosyan, A size bound for Hamilton cycles, (2011), arXiv:1107.2201 [math.CO].
[2] J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, Macmillan, London and Elsevier, New York, 1976.
[3] Zh. G. Nikoghosyan, Two sufficient conditions for Hamilton and dominating cycles, Int. J. Math. Math. Sci., 2012 (2012), Article ID 185346, 25 pages, doi:10.1155/2012/185346.
[4] K. Zhao, Dirac type condition and Hamiltonian graphs, Serdica Math. J. 37 (2011), 277–282.
[5] D. W. Cranston, S. O, Hamiltonicity in connected regular graphs, Inform. Process. Lett., 113 (2013), 858–860.

There are 5 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Article
Authors	Rao Li Anuj Daga This is me Vivek Gupta This is me Manad Mishra This is me Spandan Kumar Sahu This is me Ayush Sinha This is me
Submission Date	August 3, 2018
Acceptance Date	November 7, 2018
Publication Date	December 25, 2018
Published in Issue	Year 2018 Volume: 1 Issue: 2

Cite

APA	Li, R., Daga, A., Gupta, V., … Mishra, M. (2018). Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs. Fundamental Journal of Mathematics and Applications, 1(2), 191-193. https://doi.org/10.33401/fujma.450809
AMA	Li R, Daga A, Gupta V, Mishra M, Sahu SK, Sinha A. Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs. Fundam. J. Math. Appl. December 2018;1(2):191-193. doi:10.33401/fujma.450809
Chicago	Li, Rao, Anuj Daga, Vivek Gupta, Manad Mishra, Spandan Kumar Sahu, and Ayush Sinha. “Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs”. Fundamental Journal of Mathematics and Applications 1, no. 2 (December 2018): 191-93. https://doi.org/10.33401/fujma.450809.
EndNote	Li R, Daga A, Gupta V, Mishra M, Sahu SK, Sinha A (December 1, 2018) Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs. Fundamental Journal of Mathematics and Applications 1 2 191–193.
IEEE	R. Li, A. Daga, V. Gupta, M. Mishra, S. K. Sahu, and A. Sinha, “Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs”, Fundam. J. Math. Appl., vol. 1, no. 2, pp. 191–193, 2018, doi: 10.33401/fujma.450809.
ISNAD	Li, Rao et al. “Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs”. Fundamental Journal of Mathematics and Applications 1/2 (December2018), 191-193. https://doi.org/10.33401/fujma.450809.
JAMA	Li R, Daga A, Gupta V, Mishra M, Sahu SK, Sinha A. Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs. Fundam. J. Math. Appl. 2018;1:191–193.
MLA	Li, Rao et al. “Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 191-3, doi:10.33401/fujma.450809.
Vancouver	Li R, Daga A, Gupta V, Mishra M, Sahu SK, Sinha A. Minimum Degree and Size Conditions for Hamiltonian and Traceable Graphs. Fundam. J. Math. Appl. 2018;1(2):191-3.