Abstract
In a 6-chromatic contraction-critical graph Γ, the neighbour subgraph of a 6-vertex either contains two vertex-disjoint triangles (types A, B, C, D, E, F), or is constituted of a wheel W 6 (type J) or of a wheel W 6 with two consecutive spokes missing (type G). Here the reduction of type J is first obtained; then it is shown that the type G is incompatible with the other types. Various reductions lead to the following results: (1) The subgraph of Γ induced by the 6-vertices is either a clique or order ⩽4, or a set of mutually isolated vertices of type G. (2) Γ contains at least 20 vertices of degree 7.
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