2022/09/13 by Oleg Akchurin, Akchurin, Oleg, Svitlana Bilun +3
Computer Science · #37c10 #37c15 #37c20 #Combinatorics (math.CO) #FOS: Mathematics #G.1.7 #Geometric Topology (math.GT) #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2209.05737
openalex publication_date 2022/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is devoted to finding the colorings of the edges of the 1-skeleton of triangulations of the 2-sphere in three colors so that for each face all three of its sides have different colors. First, by the method of adding one vertex inside the triangle or on its side, we enumerate all tiangulations with no more than 8 vertices. Next, one triangulation with 6 and 7 vertices, each with two different colors, was found. And finally, it is shown that other triangulations, which have less than 8 vertices, have one coloring each.