论文信息 - On The Number Of Simple Cycles In Planar Graphs

On The Number Of Simple Cycles In Planar Graphs

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 2.27n cycles. Applying some probabilistic arguments we prove an upper bound of 3.37n.

Helmut Alt | Klaus Kriegel | Ulrich Fuchs

[1] Michael Kaufmann,et al. On Exact Solutions for the Rectilinear Steiner Tree Problem Part I: Theoretical Results , 2000, Algorithmica.

[2] G. Ringel. Map Color Theorem , 1974 .

[3] Tommy R. Jensen,et al. Graph Coloring Problems , 1994 .

[4] Michael Kaufmann,et al. On exact solutions for the rectilinear Steiner tree problem , 1997, SCG '97.

[5] R. Steinberg. The State of the Three Color Problem , 1993 .

[6] M. Blum,et al. Automata on a 2-Dimensional Tape , 1967, SWAT.

[7] Guoli Ding. Bounding the number of circuits of a graph , 1996, Comb..