| Abstract: | Having observed Tutte's classification of 3-connected graphs as those attainable from wheels by line addition and point splitting and Hedetniemi's classification of 2-connected graphs as those obtainable from K2 by line addition, subdivision and point addition, one hopes to find operations which classify n-connected graphs as those obtainable from, for example, Kn+1. In this paper I give several generalizations of the above operations and use Halin's theorem to obtain two variations of Tutte's theorem as well as a classification of 4-connected graphs. |
