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All Journal Indonesian Journal of Combinatorics
Sherlin, Intan
Institut Teknologi Bandung, Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management

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On Ramsey numbers for trees versus fans of even order Sherlin, Intan; Saputro, Suhadi Wido; Baskoro, Edy Tri; Oktariani, Finny
Indonesian Journal of Combinatorics Vol 8, No 1 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.1.2

Abstract

Given two graphs G and H. The graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or F̅ contains a copy of H. A vertex v is called a dominating vertex in a graph G if it is adjacent to all other vertices of G. A wheel Wm is a graph consisting one dominating vertex and m other vertices forming a cycle. A fan graph F1,m is a graph formed from a wheel Wm by removing one cycle-edge. In this paper, we consider the graph Ramsey number R(Tn,F1,m) of a tree Tn versus a fan F1,m. The study of R(Tn,F1,m) has been initiated by Li et. al. (2016) where Tn is a star, and continued by Sherlin et. al. (2023) for Tn which is not a star and fan F1,m with even m ≤ 8. This paper will give the graph Ramsey numbers R(Tn,F1,m) for odd m ≤ 8.
Co-Authors Edy Tri Baskoro Oktariani, Finny Saputro, Suhadi Wido