Year: 2025
Type: preprint
Abstract: Consider a directed multigraph $D$ that is balanced (i.e., at each vertex, the indegree equals the outdegree). Let $A$ be its set of arcs. Fix an integer $k$. Let $s$ be a vertex of $D$. We show that the number of $k$-element subsets $B$ of $A$ that contain no cycles but contain a path from each vertex to $s$ (we call them "$s$-convergences") is independent on $s$. This generalizes known facts about spanning arborescences, acyclic orientations and maximal acyclic subdigraphs (or, equivalently, minimum feedback arc sets). Moreover, this result can be generalized even further, replacing "contain no cycles" with "have a given set of cycles".
Source: arXiv (Cornell University)
Authors: Grinberg, Darij, Liber, Benjamin
Institution: Drexel University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979274785
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