Data structures and network algorithms
Data structures and network algorithms
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs
Journal of Algorithms
American Mathematical Monthly
On-line maintenance of the four-components of a graph (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A linear algorithm for perfect matching in hexagonal systems
Discrete Mathematics
4-connected projective-planar graphs are Hamiltonian
Journal of Combinatorial Theory Series B
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Perfect matchings in the triangular lattice
Discrete Mathematics
Maximum matchings in sparse random graphs: Karp-Sipser revisited
Random Structures & Algorithms
Converting triangulations to quadrangulations
Computational Geometry: Theory and Applications
Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Linear reductions of maximum matching
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for Petersen's matching theorem
Journal of Algorithms
Unique maximum matching algorithms
Journal of Algorithms
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Maximum matching in graphs with an excluded minor
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Computing Large Matchings in Planar Graphs with Fixed Minimum Degree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Computing large matchings in planar graphs with fixed minimum degree
Theoretical Computer Science
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In this article we present algorithms for computing large matchings in 3-regular graphs, graphs with maximum degree 3, and 3-connected planar graphs. The algorithms give a guarantee on the size of the computed matching and take linear or slightly superlinear time. Thus they are faster than the best-known algorithm for computing maximum matchings in general graphs, which runs in O(&sqrt;nm) time, where n denotes the number of vertices and m the number of edges of the given graph. For the classes of 3-regular graphs and graphs with maximum degree 3, the bounds we achieve are known to be best possible. We also investigate graphs with block trees of bounded degree, where the d-block tree is the adjacency graph of the d-connected components of the given graph. In 3-regular graphs and 3-connected planar graphs with bounded-degree 2- and 4-block trees, respectively, we show how to compute maximum matchings in slightly superlinear time.