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arXiv · 2601.16104

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

Robert Lukoťka
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Abstract

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.

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Robert Lukoťka. 2026-01-22. A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree. https://arxiv.org/abs/2601.16104

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