scholarly journals Trees of tangles in infinite separation systems

2021 ◽  
pp. 1-31
Author(s):  
CHRISTIAN ELBRACHT ◽  
JAKOB KNEIP ◽  
MAXIMILIAN TEEGEN
Keyword(s):  
Infinite Graphs ◽  
Separation Systems ◽  
Nested Sets

Abstract We present infinite analogues of our splinter lemma for constructing nested sets of separations. From these we derive several tree-of-tangles-type theorems for infinite graphs and infinite abstract separation systems.

scholarly journals Profinite Separation Systems

Order ◽  
2019 ◽  
Vol 37 (1) ◽  
pp. 179-205
Author(s):  
Reinhard Diestel ◽  
Jakob Kneip
Keyword(s):  
Basic Theory ◽  
Infinite Graphs ◽  
Additional Structure ◽  
Duality Theorems ◽  
Combinatorial Structures ◽  
Separation Systems ◽  
Abstract Setting ◽  
Future Work

AbstractSeparation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory about infinite separation systems and how they relate to the finite separation systems they induce. They can be used to prove tangle-type duality theorems for infinite graphs and matroids, which will be done in future work that will build on this paper.

scholarly journals Tangle-tree duality in abstract separation systems

2021 ◽  
Vol 377 ◽  
pp. 107470
Author(s):  
Reinhard Diestel ◽  
Sang-il Oum
Keyword(s):  
Separation Systems

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.

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