In his paper J. T. Welch [7] presents an algorithm for determining the circuits of a graph in a mechanical manner. Unfortunately, when an implementation of this procedure was attempted by N. E. Gibbs a very large class of counter examples was discovered. Gibbs rectified this situation in his algorithm [1]. However, a close study of Gibbs' algorithm shows that it is essentially an enumerative case considering all possible combinations. Hsu and Honkanen [3] developed a set of algorithms which used Welch's Concept where it applied and then examined the remaining circuits essentially in a manner like Gibbs' algorithm but did not require examining all possible combinations. R. Tarjan [6] pointed out several flaws in these algorithms which are corrected in this paper.
[1]
John T. Welch,et al.
A Mechanical Analysis of the Cyclic Structure of Undirected Linear Graphs
,
1966,
J. ACM.
[2]
Norman E. Gibbs,et al.
A Cycle Generation Algorithm for Finite Undirected Linear Graphs
,
1969,
JACM.
[3]
C. L. Liu,et al.
Introduction to Combinatorial Mathematics.
,
1971
.
[4]
Keith Paton,et al.
An algorithm for finding a fundamental set of cycles of a graph
,
1969,
CACM.
[5]
Calvin C. Gotlieb,et al.
Algorithms for finding a fundamental set of cycles for an undirected linear graph
,
1967,
CACM.