Rainbow forest consisting of short paths in Kn

Recently, the anti-Ramsey problem for disjoint union of graphs in complete graphs Kn received much attention. In particular, several researchers focused on the problem for graphs consisting of small components and in particular the problem for several forests have been investigated well. Notice that...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 376; pp. 260 - 269
Main Authors Jie, Qing, He, Menglu, Jin, Zemin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.12.2025
Subjects
Anti-Ramsey number
Linear forest
Rainbow graph
Linear forest
Rainbow graph
Anti-Ramsey number
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Summary:Recently, the anti-Ramsey problem for disjoint union of graphs in complete graphs Kn received much attention. In particular, several researchers focused on the problem for graphs consisting of small components and in particular the problem for several forests have been investigated well. Notice that previous results were always proved for large enough n. In this paper, we continue the work in this direction and consider the problem for general kP3∪tP2. We refine the bound on n and obtain the precise value of AR(Kn,kP3∪tP2) for k≥2, t≥k2−k+42 and n≥3k+2t+1.
ISSN:0166-218X
DOI:10.1016/j.dam.2025.06.041