For simple graphs G and H, their size Ramsey number (Figure presented.) is the smallest possible size of F such that for any red-blue coloring of its edges, F contains either a red G or a blue H. Similarly, we can define the connected size Ramsey number (Figure presented.) by adding the prerequisite that F must be connected. In this paper, we explore the relationships between these size Ramsey numbers and give some results on their values for certain classes of graphs. We are mainly interested in the cases where G is either a 2K 2 or a 3K 2, and where H is either a cycle Cn or a union of paths nPm. Additionally, we improve an upper bound regarding the values of (Figure presented.) and (Figure presented.) for certain t and m.
|Journal||Journal of Discrete Mathematical Sciences and Cryptography|
|Publication status||Published - 29 Mar 2022|
- Connected size Ramsey number
- Primary 05C55
- Secondary 05D10
- Size Ramsey number