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- Title
The structure of graphs with no K3,3 immersion.
- Authors
DeVos, Matt; Malekian, Mahdieh
- Abstract
The Kuratowski–Wagner Theorem asserts that a graph is planar if and only if it does not have either K3,3 or K5 as a minor. Using this, Wagner obtained a precise description of all graphs with no K3,3‐minor and all graphs with no K5‐minor. Similar results have been achieved for the class of graphs with no H‐minor for a number of small graphs H. In this paper we give a precise structure theorem for graphs which do not contain K3,3 as an immersion. This strengthens an earlier theorem of Giannopoulou, Kamiński, and Thilikos that gives a rough description of the class of graphs with no K3,3 or K5 immersion.
- Subjects
IMMERSIONS (Mathematics); PLANAR graphs
- Publication
Journal of Graph Theory, 2021, Vol 98, Issue 1, p5
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.22678