2025/10/15 by Patrick Bennett, Bennett, Patrick, Jade Nichols +1
Engineering · Physics and Astronomy · Psychology · #Color Science and Applications #Color perception and design #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2510.13382
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
A t-tone coloring of a graph G assigns to each vertex a set of t colors such that any pair of vertices u, v with distance d can share at most d-1 colors. In this note, we prove several new results on t-tone coloring. For example we prove a new result for trees of large maximum degree, as well as some results for the cartesian power of a graph. We also make a conjecture about trees.