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- W3049659404 abstract "A function $f:Nrightarrow N$ is sublinear, if [lim_{xrightarrow +infty}frac{f(x)}{x}=0.] If $A$ is an Abelian group, $G$ is a graph and $phi$ is an $A$-flow in $G$, then let $N(phi)$ be the nullity of $phi$, that is, the set of edges $e$ of $G$ with $phi(e)=0$. In this paper we show that (a) Tutte's 5-flow conjecture is equivalent to the statement that there is a sublinear function $f$, such that all $3$-edge-connected cubic graphs admit a $mathbb{Z}_5$-flow $phi$ (not necessarily no-where zero), such that $|N(phi)|leq f(|E(G)|)$; (b) Tutte's 4-flow conjecture is equivalent to the statement that there is a sublinear function $f$, such that all bridgeless graphs without a Petersen minor admit a $mathbb{Z}_4$-flow $phi$ (not necessarily no-where zero), such that $|N(phi)|leq f(|E(G)|)$; (c) Tutte's 3-flow conjecture is equivalent to the statement that there is a sublinear function $f$, such that all $4$-edge-connected graphs admit a $mathbb{Z}_3$-flow $phi$ (not necessarily no-where zero), such that $|N(phi)|leq f(|E(G)|)$." @default.
- W3049659404 created "2020-08-21" @default.
- W3049659404 creator A5054627025 @default.
- W3049659404 date "2020-08-17" @default.
- W3049659404 modified "2023-10-18" @default.
- W3049659404 title "Sublinear bounds for nullity of flows and approximating Tutte's flow conjectures." @default.
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