Graphs Drawn With Some Vertices per Face: Density and Relationships

Abstract

In addition to the content of [1], the present article: (i) contains full proofs and technical details that were omitted or only sketched in [1]; (ii) it contains a related work section; (iii) it contains a new section with results on complete graphs and complete bipartite graphs; (iv) it improves and extends the introduction and the conclusions to better motivate the subject of the paper and to highlight future research directions that can be of interest for the scientific community; (v) it extends the presentation of the results about inclusion relationships; (vi) it contains additional and revised figures, and more than 30 references in the bibliography.