THE SIZE MULTIPARTITE RAMSEY NUMBERS $m_j(P_n,K_{j\times b})$
Syafrizal Sy1, Effendi Effendi2
1Department of Mathematics
Faculty of Mathematical and Natural Science
Andalas University
Padang, 25163, INDONESIA
2 Department of Mathematics
Faculty of Mathematical and Natural Science
Andalas University
Padang - 20163, INDONESIA

Abstract


Abstract. For given two graphs $G_1$ and $G_2$, the size Ramsey multipartite numbers $m_j(G_1,G_2)$ is the smallest integer $t$ such that every factorization of graph $K_{j\times t}:=F_1\oplus F_2$ satisfies the following condition: either $F_1$ contains $G_1$ as a subgraph or $F_2$ contains $G_2$ as a subgraph. In this paper, we determine for the size multipartite Ramsey numbers $m_j(P_n,K_{j\times b})$ with integers $j,n\geq3$ and $b\geq2$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 2
Year: 2020

DOI: 10.12732/ijam.v33i2.9

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] A.P. Burger and J.H. Van Vuuren, Ramsey numbers in complete balanced multipartite graphs. Part II: Size Numbers, Discrete Math., 283 (2004), 45-49.
  2. [2] A. Gyarfas and J. Lehel, A Ramsey-type problem in directed and bipartite graphs, Periodica Math. Hungar., 3 (1973), 299-304.
  3. [3] J.H. Hattingh and M.A. Henning, Star-path bipartite Ramsey numbers, Discrete Math., 185 (1998), 255-258.
  4. [4] Syafrizal Sy, E.T. Baskoro, S. Uttunggadewa and H. Assiyatun, Path-path size multipartite Ramsey numbers, J. Combin. Math. Combin. Comput., 71 (2009), 265-271.
  5. [5] Syafrizal Sy and E.T. Baskoro, Lower bounds of the size multipartite Ramsey numbers, American Institute of Physics Proc., 1450 (2012), 259-261.