Maximal plane subgraphs of the twisted complete graph T_n that contain perfect matchings are connected under single edge exchanges.
E., Hurtado, F., Noy, M., Rivera-Campo,E.: Graphs of triangulations and perfect matchings, Graphs Combin
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A note on maximal plane subgraphs of the complete twisted graph containing perfect matchings
Maximal plane subgraphs of the twisted complete graph T_n that contain perfect matchings are connected under single edge exchanges.