Given simple graphs F, G, and H, we write F → (G, H) if for every red-blue coloring of the edges of F, there exists either a red subgraph G or a blue subgraph H in F. The size Ramsey number for G and H, denoted by f (G,H), is the smallest size of a graph F which satisfies F → (G, H). If in addition F must be connected, then the resulting number is called the connected size Ramsey number for G and H, denoted by ȓc(G,H). In this paper, we obtain upper bounds for ȓ(tK2,Pm), ȓc(tK2,Pm), ȓ(tK2,P4 + a leaf), and ȓc(tK2,P4 + a leaf) for t ≥ 1 and m ≥ 3. We also determine the exact values of fc(2K2, Pm) and f(tK2, P3). In addition, the exact values of ȓc(tK2, P3) for t = 3,4 are given.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 12 Jan 2021|
|Event||2nd Basic and Applied Sciences Interdisciplinary Conference 2018, BASIC 2018 - Depok, Indonesia|
Duration: 3 Aug 2018 → 4 Aug 2018
- Connected size Ramsey number
- Size Ramsey number