Connected Size Ramsey Numbers for The Pair Complete Graph of Order Two versus Union Complete Graph of Order Three

Hasmawati Hasmawati (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia)
Sri Indrayani (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 21 No. 2 (2025): JANUARY 2025

Let F,G, and H be finite, simple, and undirected graphs. The connected size Ramsey number r ̂_c (G,H) of graph G and H is the least integer k such that there is a connected graph F with k edges and if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of H. This paper shows that the connected size Ramsey number r ̂_c (2K_2,〖nK〗_3 )=4n+3, for n≥4.