2020/06/29 by Valeriy G. Bardakov, Akio Kawauchi, Bardakov, Valeriy G. +1
Computer Science · Mathematics · #57M07 #57M25 #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2006.16072
openalex publication_date 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, i.e. disjoint union of finite number of trees and a tangle. As a consequence we get that any finite spatial graph is a connected sum of a planar graph and a braid. Using these decompositions it is not difficult to find a set of generators and defining relations for the fundamental group of compliment of a spatial graph in 3-space ℝ3.