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Proposition: A Necessary Condition for a Graph with Shortest Cycles to Be Planar (II)

Let $k\ge 3$ be a positive integer and let $G(V,E)$ be a simple, biconnected, planar graph with $|E|$ edges and $|V|$ vertices and shortest cycle length $k.$ Then $G$ contains a vertex $v$ of degree $\deg (v)\le k+2.$

Table of Contents

Proofs: 1

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References

Bibliography

  1. Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000