We study multicolor Ramsey numbers and multicolor bipartite Ramsey numbers for caterpillar graphs, subdivided stars, and their combinations. A caterpillar graph Cₚ(a₁,…,aₚ) is a tree formed by attaching aᵢ leaves to each vertex i of a central path Pₚ . Building on results, such as the exact determination of multicolor Ramsey number of double stars, we extend these findings to more complex families, including C₃(n,m,t) , caterpillar graphs with three central vertices. For sufficiently large $$n+t$$ relative to m and odd k , we establish tight bounds and exact values of Rₖ(C₃(n,m,t)) . We further study the graph C₂(Sn₁ₙ,m) which contains a central edge, where one vertex supports a subdivided star Sn₁ₙ and the other one supports a star K1,m . Under suitable conditions, we derive the exact value of the multicolor Ramsey number of C₂(Sn₁ₙ,m) , improving known results for subdivided stars and their combinations. In bipartite settings, we determine the exact value of multicolor bipartite Ramsey number of both Sn₁ₙ and C₂(Sn₁ₙ,m) , providing results that extend and refine prior work on bipartite double stars.
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Chen et al. (2026) studied this question.