@article{chickering1995on, author = {Chickering, Max and Geiger, Dan and Heckerman, David}, title = {On Finding A Cycle Basis With A Shortest Maximal Cycle}, year = {1995}, month = {August}, abstract = {The shortest Maximal Cycle Basis (SMCB) problem is that of finding a cycle basis B of a given graph G such that the length of the longest cycle included in B is the smallest among all bases of G. We show that any cycle Basis B' of G such that the sum of the lengths of the cycles included in B' is the smallest among all cycle bases of G constitutes a solution the SMCB problem. Finding a basis with the latter property requires at most O (m3n) X steps using Horton's algorithm where m is the number of edges and n is the number of vertices.}, publisher = {Elsevier}, url = {http://approjects.co.za/?big=en-us/research/publication/on-finding-a-cycle-basis-with-a-shortest-maximal-cycle/}, pages = {55-58}, journal = {Information Processing Letters}, volume = {54}, edition = {Information Processing Letters}, }