Indonesian Journal of Combinatorics
Vol 8, No 1 (2024)

On Ramsey numbers for trees versus fans of even order

Sherlin, Intan (Institut Teknologi Bandung, Indonesia)
Saputro, Suhadi Wido (Unknown)
Baskoro, Edy Tri (Unknown)
Oktariani, Finny (Unknown)



Article Info

Publish Date
29 Jun 2024

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.

Copyrights © 2024






Journal Info

Abbrev

ijc

Publisher

Subject

Computer Science & IT Decision Sciences, Operations Research & Management

Description

Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian ...