Algebraic flow theory of infinite graphs
Babak Miraftab, Javad Moghadamzadeh
TL;DR
This paper extends algebraic flow theory from finite graphs to infinite graphs with ends, introducing new flow definitions and generalizing key theorems to broader graph classes.
Contribution
It defines A-flows and non-elusive H-flows for infinite graphs and extends classical flow theorems to these cases using abelian topological groups.
Findings
Extended flow theorems to infinite graphs with ends
Introduced A-flow and non-elusive H-flow concepts
Generalized finite graph flow results to infinite cases
Abstract
A problem by Diestel is to extend algebraic flow theory of finite graphs to infinite graphs with ends. In order to pursue this problem, we define an A-flow and non-elusive H-flow for arbitrary graphs and for abelian topological Hausdorff groups H and compact subsets A of H. We use these new definitions to extend several well-known theorems of flows in finite graphs to infinite graphs.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Topological and Geometric Data Analysis · Computability, Logic, AI Algorithms