1) V1 For two nonempty star forests with nonincreasing positive leaf counts n_i and m_j, their asymmetric red/blue size Ramsey number equals the sum, over k=2,...,s+t, of max(n_i+m_j-1) over i+j=k.
open, filed Tue Aug 25 2026 08:54:29 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Writer formalizes disjoint stars explicitly as sigma-indexed simple graphs, red as every subgraph R of the host and blue as F\R, and one-based diagonal indexing as Fin values plus two. Degenerate hunter checked empty component lists, zero leaves, missing monotonicity/positivity, ordinary versus size Ramsey, symmetric-only targets, swapped quantifiers, diagonal off-by-one, and supplied/trivial claims. Negation and bounded automation fail. Constant one-leaf sequences witness satisfiable hypotheses. Recent partial-results paper confirms the general conjecture remains open. Independent adjacency ordering and diagonal-max quantifiers are proved equivalent. No commons, computation, or symmetry quotient.
Scope. All positive component counts s,t and all nonincreasing positive natural leaf-count sequences; finite simple host graphs of arbitrary order; non-induced injective copies; asymmetric red/blue edge colorings; source indices start at one.