A separator theorem for graphs of bounded genus
Journal of Algorithms
A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
The graph genus problem is NP-complete
Journal of Algorithms
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
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
Journal of the ACM (JACM)
Journal of Combinatorial Theory Series B
Triangulating a surface with a prescribed graph
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Isomorphism of Graphs of Bounded Average Genus
SIAM Journal on Discrete Mathematics
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Embedding graphs in an arbitrary surface in linear time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Uniqueness of highly representative surface embeddings
Journal of Graph Theory
A simpler proof of the excluded minor theorem for higher surfaces
Journal of Combinatorial Theory Series B
Theoretical Computer Science - Special issue on computing and combinatorics
A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface
SIAM Journal on Discrete Mathematics
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Depth-First Search and Kuratowski Subgraphs
Journal of the ACM (JACM)
Isomorphism testing for embeddable graphs through definability
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Exponential families of non-isomorphic triangulations of complete graphs
Journal of Combinatorial Theory Series B
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Flexibility of polyhedral embeddings of graphs in surfaces
Journal of Combinatorial Theory Series B
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth 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 for graphs embeddable on the projective plane
STOC '80 Proceedings of the twelfth 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
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Some Recent Progress and Applications in Graph Minor Theory
Graphs and Combinatorics
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Canonical labelling of graphs in linear average time
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Testing graph isomorphism in parallel by playing a game
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
List-color-critical graphs on a fixed surface
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A shorter proof of the graph minor algorithm: the unique linkage theorem
Proceedings of the forty-second ACM symposium on Theory of computing
Proceedings of the forty-second ACM symposium on Theory of computing
Linkless and flat embeddings in 3-space and the unknot problem
Proceedings of the twenty-sixth annual symposium on Computational geometry
Output-sensitive algorithm for the edge-width of an embedded graph
Proceedings of the twenty-sixth annual symposium on Computational geometry
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Algorithms for the edge-width of an embedded graph
Computational Geometry: Theory and Applications
Practical graph isomorphism, II
Journal of Symbolic Computation
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For every surface S (orientable or non-orientable), we give a linear time algorithm to test the graph isomorphism of two graphs, one of which admits an embedding of face-width at least 3 into S. This improves a previously known algorithm whose time complexity is nO(g), where g is the genus of S. This is the first algorithm for which the degree of polynomial in the time complexity does not depend on g. The above result is based on two linear time algorithms, each of which solves a problem that is of independent interest. The first of these problems is the following one. Let S be a fixed surface. Given a graph G and an integer k ≥ 3, we want to find an embedding of G in S of face-width at least k, or conclude that such an embedding does not exist. It is known that this problem is NP-hard when the surface is not fixed. Moreover, if there is an embedding, the algorithm can give all embeddings of face-width at least k, up to Whitney equivalence. Here, the face-width of an embedded graph G is the minimum number of points of G in which some non-contractible closed curve in the surface intersects the graph. In the proof of the above algorithm, we give a simpler proof and a better bound for the theorem by Mohar and Robertson concerning the number of polyhedral embeddings of 3-connected graphs. The second ingredient is a linear time algorithm for map isomorphism and Whitney equivalence. This part generalizes the seminal result of Hopcroft and Wong that graph isomorphism can be decided in linear time for planar graphs.