Path-Additions of Graphs
Discrete Mathematics
2016-05-11 v1
Abstract
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes of graphs are closed under path-addition, including non-planar, right angle crossing, fan-crossing free, quasi-planar, (aligned) bar 1-visibility, and interval graphs, whereas others are not closed, including all subclasses of planar graphs, bounded treewidth, k-planar, fan-planar, outer-fan planar, outer-fan-crossing free, and bar (1,j)-visibility graphs.
Cite
@article{arxiv.1605.02891,
title = {Path-Additions of Graphs},
author = {Franz J. Brandenburg and Alexander Esch and Daniel Neuwirth},
journal= {arXiv preprint arXiv:1605.02891},
year = {2016}
}
Comments
13 pages, 2 figures