论文标题
额定性界限，以无效流量和近似Tutte的流量猜想
Sublinear bounds for nullity of flows and approximating Tutte's flow conjectures
论文作者
论文摘要
a函数$ f：n \ rightarrow n $是sublinear，如果\ [\ lim_ {x \ rightarrow +\ rightarrow +\ infty} \ frac {f（x）} {x} = 0。 $ ϕ $，即，$ g $的边缘$ e $ a $ n $ ϕ（e）= 0 $。在本文中，我们表明（a）Tutte的5-Flow猜想相当于陈述，即有sublinear函数$ f $，因此所有$ 3 $ - 与边缘连接的立方图都承认$ \ mathbb {z} _5 $ flow $ - flow $ - flow $ ϕ $（不一定是零 - 零） （b）Tutte的4-Flow猜想等同于以下陈述：有sublinear函数$ f $，使得所有没有彼得森小的无用图形都承认A $ \ mathbb {z} _4 $ -flow $ -flow $ ϕ $（不一定是零零） （c）Tutte的3流构猜想等于陈述有一个sublinear函数$ f $，因此所有$ 4 $ - 边缘连接的图形都承认A $ \ Mathbb {Z} _3 $ -Flow $ -Flow $ ϕ $（不一定是零零）
A function $f:N\rightarrow N$ is sublinear, if \[\lim_{x\rightarrow +\infty}\frac{f(x)}{x}=0.\] If $A$ is an Abelian group, $G$ is a graph and $ϕ$ is an $A$-flow in $G$, then let $N(ϕ)$ be the nullity of $ϕ$, that is, the set of edges $e$ of $G$ with $ϕ(e)=0$. 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 $ϕ$ (not necessarily no-where zero), such that $|N(ϕ)|\leq f(|E(G)|)$; (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 $ϕ$ (not necessarily no-where zero), such that $|N(ϕ)|\leq f(|E(G)|)$; (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 $ϕ$ (not necessarily no-where zero), such that $|N(ϕ)|\leq f(|E(G)|)$.
