2014/11/03 by Zdenĕk Dvořák, Dvorak, Zdenek, Paul Wollan +1 · 1 citation
Computer Science · Mathematics · #05C75 (Primary) 05C40 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #G.2.2 #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1411.0522
openalex publication_date 2014/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.