A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908782327496704 |
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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 |