Diagonal Ramsey numbers in multipartite graphs related to stars

Chula Janak Jayawardene


Abstract: Let the star on n vertices, namely K1, n − 1 be denoted by Sn. If every two coloring of the edges of a complete balanced multipartite graph Kj × s there is a copy of Sn in the first color or a copy of Sm in the second color, then we will say Kj × s → (Sn, Sm). The size Ramsey multipartite number mj(Sn, Sm) is the smallest natural number s such that Kj × s → (Sn, Sm). In this paper, we obtain the exact values of the size Ramsey numbers mj(Sn, Sm) for n, m ≥ 3 and j ≥ 3.


Ramsey numbers in multipartite graph, diagonal Ramsey number, star

Full Text:


DOI: http://dx.doi.org/10.5614/ejgta.2022.10.1.15


A.P. Burger and J.H. van Vuuren, Ramsey numbers in Complete Balanced Multipartite Graphs. Part II: Size Numbers. Discrete Mathematics, 283 (2004), 45–49.

P. Erdos, R.J. Faudree and R.H. Schelp, The size Ramsey numbers, ¨ Period Mathematics Hungary, 19 (1978), 161–173.

R.J. Faudree and R.H. Schelp, Path-path Ramsey-type numbers for the complete bipartite graph, Journal of Combinatorial Theory (B)., 19 (1975), 161–173.

C.J. Jayawardene ,E.T. Baskoro, L. Samarasekara and Syafrizal Sy, Size multipartite Ramsey numbers for stripes versus small cycles, Electronic Journal of Graph Theory and Applications 4(2) (2016), 157–170.

C.J. Jayawardene and L. Samarasekara, Size multipartite Ramsey numbers for stripes for K4 − e versus all graphs G up to 4 vertices, Annals of Pure and Applied Mathematics 13(1) (2017), 9–26.

A. Lusiani A., E.T. Baskoro, Syafrizal Sy and C.J. Jayawardene, Size multipartite Ramsey numbers for stars versus cycles, Procedia Computer Science 74 (2015), 27–31.

S.P. Radziszowski, Small Ramsey numbers, Electronic Journal of Combinatorics, (rev 14) (2014), DS1.

Syafrizal Sy, E.T. Baskoro and S. Uttunggadewa, The size multipartite Ramsey number for paths, Journal Combinatorial Mathematics and Combinatorial Computing 55 (2005), 103–107.

Syafrizal Sy, E.T. Baskoro, S. Uttunggadewa and H. Assiyatun, Path-path size multipartite Ramsey numbers, Journal Combinatorial Mathematics and Combinatorial Computing 71 (2009), 265–271.


  • There are currently no refbacks.

ISSN: 2338-2287

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View EJGTA Stats