Group Connectivity: Z_4 v. Z_2^2

11/10/2017

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by   Radek Hušek, et al.

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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 Z_2^2-connectivity does not imply 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.