On the Number of Cycles in Planar Graphs

Abstract

We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a family of graphs which have at least 2.4262 simple cycles and at least 2.0845 Hamilton cycles. Based on counting arguments for perfect matchings we prove that 2.3404 is an upper… (More)
DOI: 10.1007/978-3-540-73545-8_12

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Cite this paper

@inproceedings{Buchin2007OnTN, title={On the Number of Cycles in Planar Graphs}, author={Kevin Buchin and Christian Knauer and Klaus Kriegel and Andr{\'e} Schulz and Raimund Seidel}, booktitle={COCOON}, year={2007} }