2.5-Connectivity: Unique Components, Critical Graphs, and Applications
Abstract
If a biconnected graph stays connected after the removal of an arbitrary vertex and an arbitrary edge, then it is called 2.5-connected. We prove that every biconnected graph has a canonical decomposition into 2.5-connected components. These components are arranged in a tree-structure. We also discuss the connection between 2.5-connected components and triconnected components and use this to present a linear-time algorithm which computes the 2.5-connected components of a graph. We show that every critical 2.5-connected graph other than K4 can be obtained from critical 2.5-connected graphs of smaller order using simple graph operations. Furthermore, we demonstrate applications of 2.5-connected components in the context of cycle decompositions and cycle packings.
Cite
@article{arxiv.2003.01498,
title = {2.5-Connectivity: Unique Components, Critical Graphs, and Applications},
author = {Irene Heinrich and Till Heller and Eva Schmidt and Manuel Streicher},
journal= {arXiv preprint arXiv:2003.01498},
year = {2020}
}
Comments
18 pages, 2 figures