2017/09/27 by Hong Liu, Liu, Hong, Maryam Sharifzadeh +3
Engineering · Mathematics · #05D99 #11B75 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1709.09589
openalex publication_date 2017/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f(n,r) denote the maximum number of colourings of A ⊆ \lbrace 1,…,n\rbrace with r colours such that each colour class is sum-free. Here, a sum is a subset \lbrace x,y,z\rbrace such that x+y=z. We show that f(n,2) = 2\lceil n/2\rceil, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of f(n,r) for r ≤ 5. Similar results were obtained by Hàn and Jiménez in the setting of finite abelian groups.