Work

On a conjecture of Erdős on size Ramsey number of star forests

Year: 2024

Type: article

Abstract: Given two graphs F1 and F2, their size Ramsey number, denoted by r̂(F1, F2), is the minimum number of edges of a graph G such that for any edge coloring of G by colors red and blue, G contains either a red copy of F1 or a blue copy of F2. In this paper, we deal with the size Ramsey number of star forests (disjoint union of stars) and following a conjecture by Burr, Erdős, Faudree, Rousseau, and Schelp in 1978, we determine the exact value of r̂(⊔i = 1sK1, ni, ⊔i = 1tK1, mi) in several cases including when either mi’s and ni’s are odd, or s = 1 or s = 2 and n1 = n2.

Source: Ars Mathematica Contemporanea

DOI: 10.26493/1855-3974.3081.d6c

Authors: Akbar Davoodi, Ramin Javadi, Azam Kamranian, Ghaffar Raeisi

Institutions: Czech Academy of Sciences, Institute of Computer Science, Isfahan University of Technology, Institute for Research in Fundamental Sciences, Shahrekord University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4401816980

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Cites: 7

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Related to: 10