Fig. 5

A closed 7-chained graph is tripartite. A tripartization of the node set is given by \({\widetilde{{{\mathcal{V}}}}}_1={{\mathcal{V}}}_1\cup {{\mathcal{V}}}_3\cup {{\mathcal{V}}}_5\), \({\widetilde{{{\mathcal{V}}}}}_2={{\mathcal{V}}}_2\cup {{\mathcal{V}}}_4\cup {{\mathcal{V}}}_6\), \({\widetilde{{{\mathcal{V}}}}}_3={{\mathcal{V}}}_7\)