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

M.S.A. Bataineh; M.M.M. Jaradat; M.S. Bateeha

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 2, page 223-232
- ISSN: 2083-5892

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topM.S.A. Bataineh, M.M.M. Jaradat, and M.S. Bateeha. "The ramsey number for theta graph versus a clique of order three and four." Discussiones Mathematicae Graph Theory 34.2 (2014): 223-232. <http://eudml.org/doc/267918>.

@article{M2014,

abstract = {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},

author = {M.S.A. Bataineh, M.M.M. Jaradat, M.S. Bateeha},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Ramsey number; independent set; theta graph; complete graph},

language = {eng},

number = {2},

pages = {223-232},

title = {The ramsey number for theta graph versus a clique of order three and four},

url = {http://eudml.org/doc/267918},

volume = {34},

year = {2014},

}

TY - JOUR

AU - M.S.A. Bataineh

AU - M.M.M. Jaradat

AU - M.S. Bateeha

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

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 2

SP - 223

EP - 232

AB - 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

LA - eng

KW - Ramsey number; independent set; theta graph; complete graph

UR - http://eudml.org/doc/267918

ER -

## References

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- [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 Zbl1236.05130
- [6] J. McNamara, Sunny Brockport, unpublished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

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