Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Polynomially bounded minimization problems that are hard to approximate
Nordic Journal of Computing
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Many distances in planar graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On Two Problems in the Generation of Program Test Paths
IEEE Transactions on Software Engineering
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
A faster algorithm for computing the girth of planar and bounded genus graphs
ACM Transactions on Algorithms (TALG)
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We give a polynomial-time algorithm to find a shortest contractible cycle (i.e. a closed walk without repeated vertices) in a graph embedded in a surface. This answers a question posed by Hutchinson. In contrast, we show that finding a shortest contractible cycle through a given vertex is NP-hard. We also show that finding a shortest separating cycle in an embedded graph is NP-hard. This answers a question posed by Mohar and Thomassen.