A structure theorem for strong immersions
Combinatorics
2014-11-04 v1
Abstract
A graph H is strongly immersed in G if H is obtained from G by a sequence of vertex splittings (i.e., lifting some pairs of incident edges and removing the vertex) and edge removals. Equivalently, vertices of H are mapped to distinct vertices of G (branch vertices) and edges of H are mapped to pairwise edge-disjoint paths in G, each of them joining the branch vertices corresponding to the ends of the edge and not containing any other branch vertices. We describe the structure of graphs avoiding a fixed graph as a strong immersion.
Cite
@article{arxiv.1411.0522,
title = {A structure theorem for strong immersions},
author = {Zdenek Dvorak and Paul Wollan},
journal= {arXiv preprint arXiv:1411.0522},
year = {2014}
}
Comments
9 pages, 0 figures. arXiv admin note: text overlap with arXiv:1304.0728