Immersion in four-edge-connected graphs
Maria Chudnovsky, Zden\v{e}k Dvo\v{r}\'ak, Tereza Klimo\v{s}ov\'a,, Paul Seymour
TL;DR
This paper proves that large enough four-edge-connected graphs with high tree-width necessarily contain a g x g grid as an immersion, extending grid containment results to immersions in highly connected graphs.
Contribution
It establishes that four-edge-connected graphs of large tree-width always contain a g x g grid as an immersion, a significant extension of known results for minors.
Findings
Large four-edge-connected graphs contain g x g grid immersions
Immersions include any fixed graph with maximum degree at most four
Results have multiple applications in graph theory
Abstract
Fix g>1. Every graph of large enough tree-width contains a g x g grid as a minor; but here we prove that every four-edge-connected graph of large enough tree-width contains a g x g grid as an immersion (and hence contains any fixed graph with maximum degree at most four as an immersion). This result has a number of applications.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Interconnection Networks and Systems