Every n-vertex 7-connected 1-planar graph has at most 4n-12 edges, 4n-16 triangles, n-6 copies of K4, and thus at most 10n-33 cliques total.
Ringel, Ein Sechsfarbenproblem auf der Kugel,Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg29 (1965), 107–117
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
The maximum number of $k$-cliques of 7-connected 1-planar graphs
Every n-vertex 7-connected 1-planar graph has at most 4n-12 edges, 4n-16 triangles, n-6 copies of K4, and thus at most 10n-33 cliques total.