论文信息 - Finding and Counting Given Length Cycles (Extended Abstract)

Finding and Counting Given Length Cycles (Extended Abstract)

We present an assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs. Most of the bounds obtained depend solely on the number of edges in the graph in question, and not on the number of vertices. The bounds obtained improve upon various previously known results.

[1] Noga Alon,et al. Color-coding: a new method for finding simple paths, cycles and other small subgraphs within large graphs , 1994, STOC '94.

[2] M. Simonovits,et al. Cycles of even length in graphs , 1974 .

[3] B. Bollobás. On generalized graphs , 1965 .

[4] Norishige Chiba,et al. Arboricity and Subgraph Listing Algorithms , 1985, SIAM J. Comput..

[5] Noga Alon,et al. Color-coding , 1995, JACM.

[6] B. Monien. How to Find Long Paths Efficiently , 1985 .

[7] Frank Harary,et al. Graph Theory , 2016 .

[8] B. Bollobás,et al. Extremal Graph Theory , 2013 .

[9] Svatopluk Poljak,et al. On the complexity of the subgraph problem , 1985 .

[10] Mihalis Yannakakis,et al. The Clique Problem for Planar Graphs , 1981, Inf. Process. Lett..

[11] Leland L. Beck,et al. Smallest-last ordering and clustering and graph coloring algorithms , 1983, JACM.

[12] Dana S. Richards,et al. Finding Short Cycles in Planar Graphs Using Separators , 1986, J. Algorithms.

[13] David Eppstein,et al. The Polyhedral Approach to the Maximum Planar Subgraph Problem: New Chances for Related Problems , 1994, GD.

[14] Alon Itai,et al. Finding a Minimum Circuit in a Graph , 1978, SIAM J. Comput..

[15] Steven Skiena,et al. Recognizing small subgraphs , 1995, Networks.

[16] Dieter Kratsch,et al. Finding and Counting Small Induced Subgraphs Efficiently , 1995, WG.