A note on 1-planar graphs with minimum degree 7. (English) Zbl 1454.05029
Summary: 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.
MSC:
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
| 05C07 | Vertex degrees |
| 05C35 | Extremal problems in graph theory |
References:
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