The ramsey number for theta graph versus a clique of order three and four

• Autorzy: M.S.A. Bataineh , M.M.M. Jaradat , M.S. Bateeha
• Języki publikacji: EN

Abstrakty

EN

For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph on at least N vertices contains F1 or its complement contains F2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. We determine r(θn,Km) for m = 2, 3, 4 and n > m. More specifically, we establish that r(θn,Km) = (n − 1)(m − 1) + 1 for m = 3, 4 and n > m

Słowa kluczowe

EN

Ramsey number; independent set; theta graph; complete graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 223-232

Daty

wydano

2014-05-01

online

2014-04-12

Twórcy

autor

M.S.A. Bataineh

• Department of Mathematics Yarmouk University Irbid-Jordan

autor

M.M.M. Jaradat

• Department of Mathematics, Statistics and Physics Qatar University Doha-Qatar

autor

M.S. Bateeha

• Department of Mathematics Yarmouk University Irbid-Jordan

Bibliografia

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• [2] R. Bolze and H. Harborth, The Ramsey number r(K4 − x,K5), The Theory and Applications of Graphs (Kalamazoo, MI, 1980) John Wiley & Sons, New York (1981) 109-116.
• [3] L. Boza, Nuevas Cotas Superiores de Algunos Numeros de Ramsey del Tipo r(Km,Kn − e), in: Proceedings of the VII Jornada de Matematica Discreta y Algo- ritmica, JMDA 2010, Castro Urdiales, Spain July (2010).
• [4] R.J. Faudree, C.C. Rousseau and R.H. Schelp, All triangle-graph Ramsey numbers for connected graphs of order six , J. Graph Theory 4 (1980) 293-300. doi:10.1002/jgt.3190040307[Crossref]
• [5] M.M.M. Jaradat, M.S. Bataineh and S. Radaideh, Ramsey numbers for theta graphs, Internat. J. Combin. 2011 (2011) Article ID 649687. doi:10.1155/2011/649687
• [6] J. McNamara, Sunny Brockport, unpublished
• [7] J. McNamara and S.P. Radziszowski, The Ramsey Numbers R(K4 − e,K6 − e) and R(K4 − e,K7 − e), Congr. Numer. 81 (1991) 89-96.
• [8] S.P. Radziszowski, Small Ramsey numbers, Electron. J. Combin. (2011) DS1

Identyfikatory

DOI

10.7151/dmgt.1730