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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 Articles
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

Publication Date December 25, 2018
Submission Date August 3, 2018
Acceptance Date November 7, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Li, R., Daga, A., Gupta, V., Mishra, M., et al. (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 (December 2018), 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.
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