Journal of Prime Research in Mathematics

# Upper bounds for the size Ramsey numbers for $$P_3$$ versus $$C^{t}_{3}$$ or $$P_{n}$$

Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, 40132 Indonesia.

Y. Nuraeni
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, 40132 Indonesia.
A.A.G. Ngurah
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, 40132 Indonesia.

$$^{1}$$Corresponding Author: s304agung@math.itb.ac.id

### Abstract

In this paper, we derive an upper bound for the size Ramsey number for a path $$P_3$$ versus a friendship graph $$C_{3}^{t}$$. Furthermore, some minimal Ramsey graph for a combination $$(P_{3}, C_{3}^{t})$$is presented. We also give an upper bound of the size Ramsey number for $$P_3$$ versus $$P_n$$.

#### Keywords:

Size Ramsey number, path, friendship graph.