3-connected graphs and their degree sequences

zbMATH Open1396.05059arXiv1512.05675MaRDI QIDQ4576314

Jonathan McLaughlin

Publication date: 12 July 2018

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.

Full work available at URL: https://arxiv.org/abs/1512.05675

zbMATH Keywords

degree sequencegraph construction3-connected graphsBG-operations

Mathematics Subject Classification ID

Connectivity (05C40) Vertex degrees (05C07)

Related Items (3)

Realizing degree sequences as \(Z_3\)-connected graphs ⋮ Title not available (Why is that?) ⋮ Enumeration of the degree sequences of 3-connected graphs and cactus graphs.

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