A note on 1-planar graphs with minimum degree 7

It is well-known that 1-planar graphs have minimum degree at most 7, and not hard to see that some 1-planar graphs have minimum degree exactly 7. In this note we show that any such 1-planar graph has at least 24 vertices, and this is tight. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The article proves that any 1-planar graph with a minimum degree of 7 must contain at least 24 vertices, and this is the tightest lower bound.