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

Robert Lukoťka

A rich $k$-flow is a nowhere-zero $k$-flow $\varphi$ such that, for every pair of adjacent edges $e$ and $f$, $|\varphi (e)|\ne |\varphi (f)|$. A graph is rich flow admissible if it admits a rich $k…