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RAMSEY NUMBERS FOR CLASS OF EDGELESS, COMPLETE AND STAR GRAPHS

Yıl 2019, Cilt: 9 Sayı: 2, 220 - 224, 01.06.2019

Öz

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.

Kaynakça

  • [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] 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] M.Chundnovsky and P.Seymour, (2005), The Structure of claw-free graphs, Surveys in Combinatorics.
  • [4] Douglas B. West, (1996), Introduction to Graph Theory, Prentice Hall.
  • [5] R.L.Graham, B.L.Rothschild and J.H.Spencer, (1990), Ramsey Theory, Second Edition, Wiley.
  • [6] S.P.Radziszowski, (2014), Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey.
  • [7] F.P.Ramsey, (1930), On a problem of Formal Logic, Proc.London Math.Soc. Series 30, pp.264-286.
  • [8] J.H.Spencer, (1994), Ten Lectures on the Probabilistic Method, SIAM.
  • [9] R.Steinberg and C.A.Tovey, (1993), Planar Ramsey Numbers, J.Comb.Theory Series B, 59, pp.288- 296.
  • [10] K.Walker, (1969), The Analog of Ramsey numbers for Planar Graphs, Bull.London.Math.Sco., 1, pp.187-190.
Yıl 2019, Cilt: 9 Sayı: 2, 220 - 224, 01.06.2019

Öz

Kaynakça

  • [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] 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] M.Chundnovsky and P.Seymour, (2005), The Structure of claw-free graphs, Surveys in Combinatorics.
  • [4] Douglas B. West, (1996), Introduction to Graph Theory, Prentice Hall.
  • [5] R.L.Graham, B.L.Rothschild and J.H.Spencer, (1990), Ramsey Theory, Second Edition, Wiley.
  • [6] S.P.Radziszowski, (2014), Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey.
  • [7] F.P.Ramsey, (1930), On a problem of Formal Logic, Proc.London Math.Soc. Series 30, pp.264-286.
  • [8] J.H.Spencer, (1994), Ten Lectures on the Probabilistic Method, SIAM.
  • [9] R.Steinberg and C.A.Tovey, (1993), Planar Ramsey Numbers, J.Comb.Theory Series B, 59, pp.288- 296.
  • [10] K.Walker, (1969), The Analog of Ramsey numbers for Planar Graphs, Bull.London.Math.Sco., 1, pp.187-190.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Kaliraj K. Bu kişi benim

Naresh Kumar H. Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 2

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