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

Abstract

The notation \(tK_3\) 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 \(tK_3\). Furthermore, this result provides the computation of Ramsey number \(R(G, tK_3)\) when \(G\) is a set of disjoint paths or cycles.