On the Structure of C3-Critical Minimal 6-Connected Graphs

Аннотация

In this paper, C₃-critical minimal 6-connected graphs are studied; they are defined as 6-connected graphs, any subgraph of which obtained by edge deletion is not 6-connected and in which any clique on at most 3 vertices is contained in a 6-cutset. It is proved that more than\( \frac{5}{9} \)of all vertices of such a graph have degree 6. Bibliography: 18 titles.