2023/05/24 by Riccardo W. Maffucci, Maffucci, Riccardo W. · 2 citations
Computer Science · Engineering · #05C07 #05C10 #05C62 #05C76 #52B05 #52B10 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.15063
openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the graph degree sequences such that every realisation is a polyhedron. It turns out that there are exactly eight of them. All of these are unigraphic, in the sense that each is realised by exactly one polyhedron. This is a revisitation of a Theorem of Rao about sequences that are realised by only planar graphs. Our proof yields additional geometrical insight on this problem. Moreover, our proof is constructive: for each graph degree sequence that is not forcibly polyhedral, we construct a non-polyhedral realisation.