Harris Graphs: Tough Eulerian Graphs that are not Hamiltonian

• Eulerian graph: a connected graph where all vertices have an even degree.

• Tough graph: A graph G is tough if, for every subset S of the vertices of G, the number of components of G \ S is at most the number of vertices in S (more info here).

• Hamiltonian cycle: a path that ends at the vertex it started and visits all vertices exactly once (The first vertex is technically visited twice - once in the beginning and once at the end).

Feel free to play around with the graphs below to test the G \ S condition. To delete a vertex, right click on it and hit delete. If you find a new Harris Graph or believe that one of the graphs listed here isn't a Harris graph, fill out the Prospective Harris Graph or Error Reporting Form respectively.