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Tutte's 5-Flow Conjecture for Highly Cyclically Connected Cubic Graphs

Eckhard Steffen
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Abstract

In 1954, Tutte conjectured that every bridgeless graph has a nowhere-zero 5-flow. Let $ω$ be the minimum number of odd cycles in a 2-factor of a bridgeless cubic graph. Tutte's conjecture is equivalent to its restriction to cubic graphs with $ω\geq 2$. We show that if a cubic graph $G$ has no edge cut with fewer than $ {5/2} ω- 1$ edges that separates two odd cycles of a minimum 2-factor of $G$, then $G$ has a nowhere-zero 5-flow. This implies that if a cubic graph $G$ is cyclically $n$-edge connected and $n \geq {5/2} ω- 1$, then $G$ has a nowhere-zero 5-flow.

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BibTeXRIS

Eckhard Steffen. 2012-09-20. Tutte's 5-Flow Conjecture for Highly Cyclically Connected Cubic Graphs. https://doi.org/10.1016/j.disc.2009.03.014

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