Cyclicity of graphs
Richard H. Hammack · Journal of Graph Theory · 1999
The cyclicity of a graph is the largest integer n for which the graph is contractible to the cycle on n vertices. By analyzing the cycle space of a graph, we establish upper and lower bounds on cyclicity. These bounds facilitate the computation of cyclicity for several classes of graphs, including chordal graphs, complete n-partite graphs, n-cubes, products of trees and cycles, and planar graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 160–170, 1999