A Linear-Time Algorithm for Finding a Maximal Planar Subgraph

Authors:
Hristo N. Djidjev
Affiliations:
-
Venue:
SIAM Journal on Discrete Mathematics
Year:
2006

Citing 0
Cited 3

Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

Theoretical Computer Science
A self-stabilizing algorithm for the maximum planarization problem in complete bipartite networks

Information Processing Letters
Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics

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Abstract

We construct an optimal linear-time algorithm for the maximal planar subgraph problem: given a graph G, find a planar subgraph G' of G such that adding to G' an extra edge of G results in a nonplanar graph. Our solution is based on a fast data structure for incremental planarity testing of triconnected graphs and a dynamic graph search procedure. Our algorithm can be transformed into a new optimal planarity testing algorithm.