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Hilda Assiyatun
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
Electrical & Electronics Engineering

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The connected size Ramsey number for matchings versus small disconnected graphs Hilda Assiyatun; Budi Rahadjeng; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.1.9

Abstract

Let F, G,  and H be simple graphs. The notation F → (G, H) means that if all the edges of F are arbitrarily colored by red or blue, then there always exists either a red subgraph G or a blue subgraph H. The size Ramsey number of graph G and H,  denoted by r̂(G, H) is the smallest integer k such that there is a graph F with k edges satisfying F → (G, H). In this research, we will study a modified size Ramsey number, namely the connected size Ramsey number. In this case, we only consider connected graphs F satisfying the above properties. This connected size Ramsey number of G and H is denoted by r̂c(G, H). We will derive an upper bound of r̂c(nK2, H), n ≥ 2 where H is 2Pm or 2K1, t,  and find the exact values of r̂c(nK2, H),  for some fixed n.
Co-Authors BUDI RAHADJENG Edy Tri Baskoro