Rao's Theorem for forcibly planar sequences revisited
Combinatorics
2023-05-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2305.15063,
title = {Rao's Theorem for forcibly planar sequences revisited},
author = {Riccardo W. Maffucci},
journal= {arXiv preprint arXiv:2305.15063},
year = {2023}
}