A constructive characterization of uniformly 4-connected graphs

A constructive characterization of the class of uniformly $4$-connected graphs is presented. The characterization is based on the application of graph operations to appropriate vertex and edge sets in uniformly $4$-connected graphs, that is, any uniformly $4$-connected graph can be obtained from $C_5^2$ or $C_6^2$ by a number of ${\mathrm{\Delta }}_1^{+}$ or ${\mathrm{\Delta }}_2^{+}$-operations to quasi $4$-compatible sets.