# Excluding Graphs as Immersions in Surface Embedded Graphs

5 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We prove a structural characterization of graphs that forbid a fixed graph $H$ as an immersion and can be embedded in a surface of Euler genus $\gamma$. In particular, we prove that a graph $G$ that excludes some connected graph $H$ as an immersion and is embedded in a surface of Euler genus $\gamma$ has either "small" treewidth (bounded by a function of $H$ and $\gamma$) or "small" edge connectivity (bounded by the maximum degree of $H$). Using the same techniques we also prove an excluded grid theorem on bounded genus graphs for the immersion relation.
Type de document :
Pré-publication, Document de travail
2013
Domaine :

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00805139
Contributeur : Dimitrios M. Thilikos <>
Soumis le : mercredi 27 mars 2013 - 10:56:18
Dernière modification le : vendredi 5 octobre 2018 - 21:14:01

### Identifiants

• HAL Id : lirmm-00805139, version 1
• ARXIV : 1303.6567

### Citation

Archontia C. Giannopoulou, Marcin Kaminski, Dimitrios M. Thilikos. Excluding Graphs as Immersions in Surface Embedded Graphs. 2013. 〈lirmm-00805139〉

### Métriques

Consultations de la notice