Nonnegative matrices and other topics in linear algebra
Nonnegative matrices and other topics in linear algebra
On the Number of Simple Cycles in Planar Graphs
Combinatorics, Probability and Computing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the number of crossing-free matchings, (cycles, and partitions)
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Random triangulations of planar point sets
Proceedings of the twenty-second annual symposium on Computational geometry
Contour grouping and abstraction using simple part models
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
On the number of spanning trees a planar graph can have
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Optimizing regular edge labelings
GD'10 Proceedings of the 18th international conference on Graph drawing
Spatiotemporal contour grouping using abstract part models
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
Disjoint compatible geometric matchings
Proceedings of the twenty-seventh annual symposium on Computational geometry
Counting plane graphs: flippability and its applications
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Interpolating an unorganized 2D point cloud with a single closed shape
Computer-Aided Design
Counting plane graphs: perfect matchings, spanning cycles, and Kasteleyn's technique
Proceedings of the twenty-eighth annual symposium on Computational geometry
Computational geometry column 54
ACM SIGACT News
Counting plane graphs: Perfect matchings, spanning cycles, and Kasteleyn's technique
Journal of Combinatorial Theory Series A
Counting plane graphs: cross-graph charging schemes
GD'12 Proceedings of the 20th international conference on Graph Drawing
A simple aggregative algorithm for counting triangulations of planar point sets and related problems
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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 growth from 1.03 to 0.46.