Quasi-4-Connected Components
Discrete Mathematics
2016-02-16 v1 Data Structures and Algorithms
Combinatorics
Abstract
We introduce a new decomposition of a graphs into quasi-4-connected components, where we call a graph quasi-4-connected if it is 3-connected and it only has separations of order 3 that remove a single vertex. Moreover, we give a cubic time algorithm computing the decomposition of a given graph. Our decomposition into quasi-4-connected components refines the well-known decompositions of graphs into biconnected and triconnected components. We relate our decomposition to Robertson and Seymour's theory of tangles by establishing a correspondence between the quasi-4-connected components of a graph and its tangles of order 4.
Cite
@article{arxiv.1602.04505,
title = {Quasi-4-Connected Components},
author = {Martin Grohe},
journal= {arXiv preprint arXiv:1602.04505},
year = {2016}
}