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Main Authors: Li, Zhenzhi, Shen, Wujie
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.09153
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author Li, Zhenzhi
Shen, Wujie
author_facet Li, Zhenzhi
Shen, Wujie
contents We study the structure of the space $Ω_3(G)$ of $\partial$-invariant 3-paths in a directed graph $G$. We prove that $Ω_3(G)$ admits a basis consisting of trapezohedral paths $τ_m$ ($m \ge 2$) and their merging images. Moreover, we provide an explicit construction of such a basis and, as a consequence, obtain an algorithm with time complexity $O(|V(G)|^5)$ for computing the dimension and a basis of $Ω_3(G)$ for any finite digraph.
format Preprint
id arxiv_https___arxiv_org_abs_2603_09153
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle $\partial$-invariant path generators for digraphs
Li, Zhenzhi
Shen, Wujie
Combinatorics
We study the structure of the space $Ω_3(G)$ of $\partial$-invariant 3-paths in a directed graph $G$. We prove that $Ω_3(G)$ admits a basis consisting of trapezohedral paths $τ_m$ ($m \ge 2$) and their merging images. Moreover, we provide an explicit construction of such a basis and, as a consequence, obtain an algorithm with time complexity $O(|V(G)|^5)$ for computing the dimension and a basis of $Ω_3(G)$ for any finite digraph.
title $\partial$-invariant path generators for digraphs
topic Combinatorics
url https://arxiv.org/abs/2603.09153