RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS

Volume: 9 Number: 2 June 1, 2019
  • Kaliraj K.
  • Naresh Kumar H.
EN

RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS

Abstract

For any graph class G of any two positive integers i and j, the Ramsey number RG i; j is the smallest integer such that every graph in G on atleast RG i; j vertices has a clique of size i or an independent set of size j. In this paper, we found the Ramsey numbers for the graph class of edgeless graphs, complete graphs, star graphs and class of all edgeless and complete graphs.

Keywords

References

  1. [1] R.Belmonte, P.Heggernes, P.Van’t Hof and R.Saei, (2012), Ramsey numbers for Line and Perfect Graphs, COCOON 2012 Springer , LNCS 7434: pp.204-215.
  2. [2] R.Belmonte, P.Heggernes, P.Van’t Hof and R.Saei, (2014), Graph Class and Ramsey Numbers, Discrete Applied Mathematics, Volume 173, pp.16-27.
  3. [3] M.Chundnovsky and P.Seymour, (2005), The Structure of claw-free graphs, Surveys in Combinatorics.
  4. [4] Douglas B. West, (1996), Introduction to Graph Theory, Prentice Hall.
  5. [5] R.L.Graham, B.L.Rothschild and J.H.Spencer, (1990), Ramsey Theory, Second Edition, Wiley.
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  7. [7] F.P.Ramsey, (1930), On a problem of Formal Logic, Proc.London Math.Soc. Series 30, pp.264-286.
  8. [8] J.H.Spencer, (1994), Ten Lectures on the Probabilistic Method, SIAM.

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Kaliraj K. This is me

Naresh Kumar H. This is me

Publication Date

June 1, 2019

Submission Date

-

Acceptance Date

-

Published in Issue

Year 2019 Volume: 9 Number: 2

APA
K., K., & H., N. K. (2019). RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS. TWMS Journal of Applied and Engineering Mathematics, 9(2), 220-224. https://izlik.org/JA72LS39UJ
AMA
1.K. K, H. NK. RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS. JAEM. 2019;9(2):220-224. https://izlik.org/JA72LS39UJ
Chicago
K., Kaliraj, and Naresh Kumar H. 2019. “RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 9 (2): 220-24. https://izlik.org/JA72LS39UJ.
EndNote
K. K, H. NK (June 1, 2019) RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS. TWMS Journal of Applied and Engineering Mathematics 9 2 220–224.
IEEE
[1]K. K. and N. K. H., “RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS”, JAEM, vol. 9, no. 2, pp. 220–224, June 2019, [Online]. Available: https://izlik.org/JA72LS39UJ
ISNAD
K., Kaliraj - H., Naresh Kumar. “RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 9/2 (June 1, 2019): 220-224. https://izlik.org/JA72LS39UJ.
JAMA
1.K. K, H. NK. RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS. JAEM. 2019;9:220–224.
MLA
K., Kaliraj, and Naresh Kumar H. “RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS”. TWMS Journal of Applied and Engineering Mathematics, vol. 9, no. 2, June 2019, pp. 220-4, https://izlik.org/JA72LS39UJ.
Vancouver
1.Kaliraj K., Naresh Kumar H. RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS. JAEM [Internet]. 2019 Jun. 1;9(2):220-4. Available from: https://izlik.org/JA72LS39UJ