scholarly journals Menger's theorem for infinite graphs with ends

2005 ◽  
Vol 50 (3) ◽  
pp. 199-211 ◽  
Author(s):  
Henning Bruhn ◽  
Reinhard Diestel ◽  
Maya Stein
Keyword(s):  
Infinite Graphs ◽  
Menger's Theorem

Menger's Theorem for a Countable Source Set

1994 ◽  
Vol 3 (2) ◽  
pp. 145-156 ◽  
Author(s):  
Ron Aharoni ◽  
Reinhard Diestel
Keyword(s):  
Infinite Graph ◽  
Infinite Graphs ◽  
Disjoint Paths ◽  
Menger's Theorem

Paul Erdős has conjectured that Menger's theorem extends to infinite graphs in the following way: whenever A, B are two sets of vertices in an infinite graph, there exist a set of disjoint A−B paths and an A−B separator in this graph such that the separator consists of a choice of precisely one vertex from each of the paths. We prove this conjecture for graphs that contain a set of disjoint paths to B from all but countably many vertices of A. In particular, the conjecture is true when A is countable.

scholarly journals Menger’s theorem for infinite graphs

2008 ◽  
Vol 176 (1) ◽  
pp. 1-62 ◽  
Author(s):  
Ron Aharoni ◽  
Eli Berger
Keyword(s):  
Infinite Graphs ◽  
Menger's Theorem

A constraint-based approach to solving games on infinite graphs

2014 ◽  
Vol 49 (1) ◽  
pp. 221-233 ◽  
Author(s):  
Tewodros Beyene ◽  
Swarat Chaudhuri ◽  
Corneliu Popeea ◽  
Andrey Rybalchenko
Keyword(s):  
Infinite Graphs

scholarly journals A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

2019 ◽  
Vol 22 (5) ◽  
pp. 837-844
Author(s):  
Gareth Wilkes
Keyword(s):  
Fundamental Group ◽  
Infinite Graphs ◽  
Graphs Of Groups ◽  
Arbitrary Graphs

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.

scholarly journals Divisors and the spectrum of infinite graphs

1987 ◽  
Vol 91 ◽  
pp. 99-106 ◽  
Author(s):  
Bojan Mohar ◽  
Matjaž Omladič
Keyword(s):  
Infinite Graphs
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