2024/10/07 by Mitchell Minyard, Minyard, Mitchell, Mark R. Sepanski +1 · 2 citations
Decision Sciences · Engineering · #05C70 #05C75 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05C15 #Scheduling and Timetabling Solutions #Secondary: 05C69 #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2410.05422
openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph is said to be neighborhood 3-balanced if there exists a vertex labeling with three colors so that each vertex has an equal number of neighbors of each color. We give order constraints on 3-balanced graphs, determine which generalized Petersen and Pappus graphs are 3-balanced, discuss when being 3-balanced is preserved under various graph constructions, give two general characterizations of cubic 3-balanced graphs, and classify cubic 3-balanced graphs of small order.