English

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.

Keywords

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

R2 v1 2026-06-22T13:57:11.022Z