Topological infinite gammoids, and a new Menger-type theorem for infinite graphs
The electronic journal of combinatorics, Tome 25 (2018) no. 3
Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid.As our main tool, we prove for any infinite graph $G$ with vertex-sets $A$ and $B$, if every finite subset of $A$ is linked to $B$ by disjoint paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint paths or rays in a natural topology on $G$ and its ends.This latter theorem implies the topological Menger theorem of Diestel for locally finite graphs. It also implies a special case of the infinite Menger theorem of Aharoni and Berger.
DOI :
10.37236/6083
Classification :
05C63
Mots-clés : gammoids, infinite graph, ends, topological infinite graph theory, Menger's theorem
Mots-clés : gammoids, infinite graph, ends, topological infinite graph theory, Menger's theorem
Affiliations des auteurs :
Johannes Carmesin 1
@article{10_37236_6083,
author = {Johannes Carmesin},
title = {Topological infinite gammoids, and a new {Menger-type} theorem for infinite graphs},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/6083},
zbl = {1395.05117},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6083/}
}
Johannes Carmesin. Topological infinite gammoids, and a new Menger-type theorem for infinite graphs. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/6083
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