Size multipartite Ramsey numbers for stripes versus small cycles

Chula Janak Jayawardene (Department of Mathematics, University of Colombo, Colombo, Sri Lanka)
Edy Tri Baskoro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Lilanthi Samarasekara (Department of Mathematics, University of Colombo, Colombo, Sri Lanka)
Syafrizal Sy (Universitas Andalas, Padang, Indonesia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications

For simple graphs $G_1$ and $G_2$, the size Ramsey multipartite number $m_j(G_1, G_2)$ is defined as the smallest natural number $s$ such that any arbitrary two coloring of the graph $K_{j \times s}$ using the colors red and blue, contains a red $G_1$ or a blue $G_2$ as subgraphs. In this paper, we obtain the exact values of the size Ramsey numbers $m_j(nK_2, C_m)$ for $j \ge 2$ and $m \in \{3,4,5,6\}$.