Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Transforming curves on surfaces
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
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
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
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
Finding shortest contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
Output-sensitive algorithm for the edge-width of an embedded graph
Proceedings of the twenty-sixth annual symposium on Computational geometry
Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
ACM Transactions on Algorithms (TALG)
Computing the Shortest Essential Cycle
Discrete & Computational Geometry
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Annotating simplices with a homology basis and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
An efficient computation of handle and tunnel loops via Reeb graphs
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Let $G$ be a graph cellularly embedded on a surface $\mathcal{S}$. We consider the problem of determining whether $G$ contains a cycle (i.e., a closed walk without repeated vertices) of a certain topological type in $\mathcal{S}$. We show that the problem can be answered in linear time when the topological type is one of the following: contractible, noncontractible, or nonseparating. In each case, we obtain the same time complexity if we require the cycle to contain a given vertex. On the other hand, we prove that the problem is NP-complete when considering separating or splitting cycles. We also show that deciding the existence of a separating or a splitting cycle of length at most $k$ is fixed-parameter tractable with respect to $k$ plus the genus of the surface.