2026/07/27 by Cheng Chi, Jialin He, Fuhong Ma
Mathematics · #math.CO
For a graph H with 3| e(H), the zero-sum Ramsey number R(H,\Z3) is the least integer N such that every labeling of the edges of KN by elements of \Z3 contains a copy of H whose edge labels sum to zero. We determine the last previously unresolved infinite family in the complete-graph case modulo 3. More precisely, we prove that \(R(Kn,\Z3)=n+3\) for every n≥ 10 satisfying n≡ 1\pmod 3. Consequently, for k≥ 1, \(R(K9k+7,\Z3)=9k+10\), resolving a problem of Caro and Mifsud.