A triangle-replaced graph T(G) is a cubic graph in which each vertex is replaced by a triangle graph such that each vertex of the triangle is connected to one of the originally adjacent vertices of a graph G. The triangle-replaced Coxeter graph appears as an exceptional graph in conjectures about nonhamiltonian vertex-transitive graphs, H^*-connected graphs, and Hamilton decompositions.

Coxeter graph | Hamilton decomposition | H^*-connected graph | nonhamiltonian vertex-transitive graph | Petersen graph