Rainbow short linear forests in edge-colored complete graph

An edge-colored graph G is called rainbow if no two edges of G have the same color. For a graph G and a subgraph H⊆G, the anti-Ramsey number AR(G,H) is the maximum number of colors in an edge-coloring of G such that G contains no rainbow copy of H. Recently, the anti-Ramsey problem for disjoint unio...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 361; pp. 523 - 536
Main Authors He, Menglu, Jin, Zemin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 30.01.2025
Subjects
Anti-Ramsey number
Matching
Path
Rainbow graph
Path
Matching
Anti-Ramsey number
Rainbow graph
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Summary:An edge-colored graph G is called rainbow if no two edges of G have the same color. For a graph G and a subgraph H⊆G, the anti-Ramsey number AR(G,H) is the maximum number of colors in an edge-coloring of G such that G contains no rainbow copy of H. Recently, the anti-Ramsey problem for disjoint union of graphs received much attention. In particular, several researchers focused on the problem for graphs consisting of small components. In this paper, we continue the work in this direction. We refine the bound and obtain the precise value of AR(Kn,P3∪tP2) for all n≥2t+3. Additionally, we determine the value of AR(Kn,2P3∪tP2) for any integers t≥1 and n≥2t+7.
ISSN:0166-218X
DOI:10.1016/j.dam.2024.11.002