The Goodness of Path or Cycle with Respect to Multiple Copies of Complete Graphs of Order Three

Abstract

The notation $t{K}_3$ represents a graph with $t$ copies of the complete graph $K_3$. In this note, we discuss the goodness of path $P_n$ or cycle $C_n$ with respect to $t{K}_3$. Furthermore, this result provides the computation of Ramsey number $R(G,t{K}_3)$ when $G$ is a set of disjoint paths or cycles.