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
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