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arXiv · 1711.03895

Group Connectivity: $\mathbb Z_4$ v. $\mathbb Z_2^2$

Radek Hušek·Lucie Mohelníková·Robert Šámal
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Abstract

We answer a question on group connectivity suggested by Jaeger et al. [Group connectivity of graphs -- A nonhomogeneous analogue of nowhere-zero flow properties, JCTB 1992]: we find that $\mathbb Z_2^2$-connectivity does not imply $\mathbb Z_4$-connectivity, neither vice versa. We use a computer to find the graphs certifying this and to verify their properties using non-trivial enumerative algorithm. While the graphs are small (the largest has 15 vertices and 21 edges), a computer-free approach remains elusive.

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Radek Hušek, Lucie Mohelníková, Robert Šámal. 2017-11-10. Group Connectivity: $\mathbb Z_4$ v. $\mathbb Z_2^2$. https://arxiv.org/abs/1711.03895

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