An Optimal Algorithm to Detect a Line Graph and Output Its Root Graph

Authors:
Philippe G. H. Lehot
Affiliations:
Fireman's Fund American Insurance Companies, P.O. Box 3395, San Francisco, California
Venue:
Journal of the ACM (JACM)
Year:
1974

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Abstract

Given a graph H with E edges and N nodes, a graph G is sought such that H is the line graph of G, if G exists. The algorithm does this within the order of E steps, in fact in E + O(N) steps. This algorithm is optimal in its complexity.