Ramsey numbers of Ks + mKt versus Kn
Abstract
For integers m >= 1, s >= 0, and t >= 1, let Ks + mKt denote the join of a clique Ks and m vertex-disjoint copies of Kt. We prove that for fixed m >= 1, t >= 1, and s >= 0, R(Ks + mKt, Kn) = O( ns+t-1 / (log n)s+t-2 ). This settles a problem proposed by Liu and Li (2026). Moreover, for (s,t) = (0,3) the bound is tight up to a constant factor, matching the classical result R(K3, Kn) = Theta( n2 / log n ) of Kim (1995).
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.