On the Space of 2-Linkages
Guantao Chen, Serguei Norine, Robin Thomas, Hein van der, Holst

TL;DR
This paper investigates the algebraic structure of 2-linkages in graphs, providing characterizations of when certain path span modules are proper subsets of a related module, under high connectivity conditions.
Contribution
It offers new characterizations of the space of 2-linkages in highly connected graphs, advancing understanding of their algebraic and combinatorial properties.
Findings
Characterizations of when $P(G; R, S)$ is a proper subset of $L(R, S)$
Results depend on the connectivity level of the graph
Provides conditions for the algebraic structure of 2-linkages
Abstract
Let be a finite undirected graph. If is an oriented path from to , we define . If , we denote by the span of the set of all with and disjoint oriented paths of connecting vertices in and , respectively. By , we denote the submodule of consisting all such that for all , for all , and for all . In this paper, we provide, when is sufficiently connected, characterizations when is a proper subset of .
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Advanced Differential Equations and Dynamical Systems
