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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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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Abstract 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.
AbstractList 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.
Author Jie, Qing
He, Menglu
Jin, Zemin
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Keywords Linear forest
Rainbow graph
Anti-Ramsey number
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Snippet Recently, the anti-Ramsey problem for disjoint union of graphs in complete graphs Kn received much attention. In particular, several researchers focused on the...
SourceID elsevier
SourceType Publisher
StartPage 260
SubjectTerms Anti-Ramsey number
Linear forest
Rainbow graph
Title Rainbow forest consisting of short paths in Kn
URI https://dx.doi.org/10.1016/j.dam.2025.06.041
Volume 376
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