Solving Rectilinear Steiner Tree Problems Exactly in Theory and Practice
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Cyclic pattern kernels for predictive graph mining
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
On the number of crossing-free matchings, (cycles, and partitions)
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the number of cycles in planar graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Let C(G) denote the number of simple cycles of a graph G and let C(n) be the maximum of C(G) over all planar graphs with n nodes. We present a lower bound on C(n), constructing graphs with at least 2.28n cycles. Applying some probabilistic arguments we prove an upper bound of 3.37n.We also discuss this question restricted to the subclasses of grid graphs, bipartite graphs, and 3-colourable triangulated graphs.