Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-01-09 , DOI: 10.1016/j.disc.2019.111809
Jiaao Li; Xueliang Li; Meiling Wang

We prove that for a simple graph $G$ with $|V\left(G\right)|\ge 32$, if $min\left\{\delta \left(G\right),\delta \left({G}^{c}\right)\right\}\ge 4$, then either $G$ or its complementary graph ${G}^{c}$ has flow index strictly less than 3. This is proved by a newly developed closure operation, which may be useful in studying further flow index problems. In particular, our result supports a recent conjecture of Li et al. (2018), and improves a result of Hou et al. (2012) on nowhere-zero 3-flows.

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