Group connectivity: Z_4 vs Z_2^2

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10403201" target="_blank" >RIV/00216208:11320/20:10403201 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=f4ZNxHB4wY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=f4ZNxHB4wY</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22488" target="_blank" >10.1002/jgt.22488</a>

Result language
angličtina
Original language name
Group connectivity: Z_4 vs Z_2^2
Original language description
We answer a question on group connectivity suggested by Jaeger et al [J. Combin. Theory, Ser. B 56 (1992), pp. 165-182]: 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 a nontrivial enumerative algorithm (and we also use an independent implementation of a straightforward algorithm to double-check our results). We provide a simple construction to provide an infinite family of examples. While the graphs we found are small (the largest has 15 vertices and 21 edges), a computer-free approach remains elusive.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-21082S" target="_blank" >GA19-21082S: Graphs and their algebraic properties</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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