Topological Infinite Gammoids, and a New Menger-Type Theorem for Infinite Graphs
Keyword(s):
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.
Keyword(s):
2001 ◽
Vol 131
(3)
◽
pp. 427-443
◽
Keyword(s):
2000 ◽
Vol 10
(05)
◽
pp. 591-602
◽
Keyword(s):
2006 ◽
Vol 96
(2)
◽
pp. 302-312
◽
2008 ◽
Vol 22
(4)
◽
pp. 1381-1392
◽
1983 ◽
Vol 34
(1)
◽
pp. 48-57
◽