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Song, Ruyu
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Electrical & Electronics Engineering

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Connected size Ramsey numbers of matchings versus a small path or cycle Wang, Sha; Song, Ruyu; Zhang, Yixin; Zhang, Yanbo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 1 (2025): 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.2025.13.1.11

Abstract

Given two graphs G1, G2, the connected size Ramsey number rc(G1, G2) is defined to be the minimum number of edges of a connected graph G, such that for any red-blue edge colouring of G, there is either a red copy of G1 or a blue copy of G2. Concentrating on rc(nK2, G2) where nK2 is a matching, we generalise and improve two previous results as follows. Vito, Nabila, Safitri, and Silaban (J. Phys. Conf. Ser., 2021) obtained the exact values of rc(nK2, P3) for n = 2, 3, 4. We determine its exact values for all positive integers n. Rahadjeng, Baskoro, and Assiyatun (Proc. Indian Acad. Sci.: Math. Sci., 2017) proved that rc(nK2, C4)≤5n − 1 for n ≥ 4. We improve the upper bound from 5n − 1 to ⌊(9n − 1)/2⌋. In addition, we show a result which has the same flavour and has exact values: rc(nK2, C3)=4n − 1 for all positive integers n.
Co-Authors Wang, Sha Zhang, Yanbo Zhang, Yixin