Minimal Nontoroidal Graphs on Eight Vertices

Abstract

Using the technique of embedding, we prove that the graphs obtained from 8 K , the complete graph on eight vertices, by deleting the edges of 3 K , a triangle, or 2,3 K , the complete bipartite graph with 2 vertices and 3 vertices, or 2 2 3 K K P   , the disjoint union of two paths of length one and one path of length two, are minimal nontoroidal graphs.