A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree

Fuente: arXiv
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Main Author: Lukoťka, Robert
Format: Preprint
Published: 2026
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author Lukoťka, Robert
author_facet Lukoťka, Robert
contents A rich $k$-flow is a nowhere-zero $k$-flow $ϕ$ such that, for every pair of adjacent edges $e$ and $f$, $|ϕ(e)| \neq |ϕ(f)|$. A graph is rich flow admissible if it admits a rich $k$-flow for some integer $k$. In this paper, we prove that if $G$ is a rich flow admissible graph with maximum degree $Δ$, then $G$ admits a rich $(264Δ- 445)$-flow.
format Preprint
id arxiv_https___arxiv_org_abs_2601_16104
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree
Lukoťka, Robert
Combinatorics
05C21
G.2.1
A rich $k$-flow is a nowhere-zero $k$-flow $ϕ$ such that, for every pair of adjacent edges $e$ and $f$, $|ϕ(e)| \neq |ϕ(f)|$. A graph is rich flow admissible if it admits a rich $k$-flow for some integer $k$. In this paper, we prove that if $G$ is a rich flow admissible graph with maximum degree $Δ$, then $G$ admits a rich $(264Δ- 445)$-flow.
title A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree
topic Combinatorics
05C21
G.2.1
url https://arxiv.org/abs/2601.16104