Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
On short noncontractible cycles in embedded graphs
SIAM Journal on Discrete Mathematics
Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Five-coloring maps on surfaces
Journal of Combinatorial Theory Series B
Computing the orientable genus of projective graphs
Journal of Graph Theory
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Flexibility of polyhedral embeddings of graphs in surfaces
Journal of Combinatorial Theory Series B
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Graph and map isomorphism and all polyhedral embeddings in linear time
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Locally planar graphs are 5-choosable
Journal of Combinatorial Theory Series B
Algorithms for finding an induced cycle in planar graphs and bounded genus graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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)
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Let G be an unweighted graph of complexity n embedded in a surface of genus g, orientable or not. We describe improved algorithms to compute a shortest non-contractible and a shortest non-separating cycle in G. If k is an integer, we can compute such a non-trivial cycle with length at most k in O(gnk) time, or correctly report that no such cycle exists. In particular, on a fixed surface, we can test in linear time whether the edge-width or face-width of a graph is bounded from above by a constant. This also implies an output-sensitive algorithm to compute a shortest non-trivial cycle that runs in O(gnk"0) time, where k"0 is the length of the cycle. We also give an approximation algorithm for the shortest non-trivial cycle. If a parameter 0