3-connected graphs and their degree sequences

Abstract

Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence can only be realised as a 3-connected graph. Finally, a matrix is introduced whose non-empty entries partition the set of 3-connected graphs.

11 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1512.01377