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COCOON
2007
Springer

On the Number of Cycles in Planar Graphs

13 years 9 months ago
On the Number of Cycles in Planar Graphs
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 2.4262n simple cycles and at least 2.0845n Hamilton cycles. Based on counting arguments for perfect matchings we prove that 2.3404n is an upper bound for the number of Hamiltonian cycles. Moreover, we obtain upper bounds for the number of simple cycles of a given length with a face coloring technique. Combining both, we show that there is no planar graph with more than 2.8927n simple cycles. This reduces the previous gap between the upper and lower bound for the exponential
Kevin Buchin, Christian Knauer, Klaus Kriegel, And
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Where COCOON
Authors Kevin Buchin, Christian Knauer, Klaus Kriegel, André Schulz, Raimund Seidel
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