Errors in graph embedding algorithms

Authors:
Wendy Myrvold;William Kocay
Affiliations:
Dept. of Computer Science, University of Victoria, Victoria, B.C., Canada, V8W 3P6;Computer Science Department, St. Paul's College, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2
Venue:
Journal of Computer and System Sciences
Year:
2011

Citing 17
Cited 1

An efficient algorithm for embedding graphs in the projective plane

Graph theory with applications to algorithms and computer science
An efficient algorithm for the genus problem with explicit construction of forbidden subgraphs

STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Projective planarity in linear time

Journal of Algorithms
Embedding graphs in an arbitrary surface in linear time

STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Fast generation of cubic graphs

Journal of Graph Theory
A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface

SIAM Journal on Discrete Mathematics
A new planarity test

Theoretical Computer Science
Practical toroidality testing

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Efficient Planarity Testing

Journal of the ACM (JACM)
Note on Hopcroft and Tarjan's Planarity Algorithm

Journal of the ACM (JACM)
Embedding Graphs in the Torus in Linear Time

Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
An efficient algorithm for determining whether a cubic graph is toroidal

STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On determining the genus of a graph in O(v O(g)) steps(Preliminary Report)

STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus

STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus

STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Graphs, Algorithms and Optimization

Graphs, Algorithms and Optimization
Additional PC-Tree planarity conditions

GD'04 Proceedings of the 12th international conference on Graph Drawing

Practical graph isomorphism, II

Journal of Symbolic Computation

Quantified Score

Hi-index	0.01

Visualization

Abstract

One major area of difficulty in developing an algorithm for embedding a graph on a surface is handling bridges which have more than one possible placement. This paper addresses a number of published algorithms where this has not been handled correctly. This problem arises in certain presentations of the Demoucron, Malgrange and Pertuiset planarity testing algorithm. It also occurs in an algorithm of Filotti for embedding 3-regular graphs on the torus. The same error appears in an algorithm for embedding graphs of arbitrary genus by Filotti, Miller and Reif. It is also present in an algorithm for embedding graphs of arbitrary genus by Djidjev and Reif. The omission regarding the Demoucron, Malgrange and Pertuiset planarity testing algorithm is easily remedied. However there appears to be no way of correcting the algorithms of the other papers without making the algorithms take exponential time.