Matching is as easy as matrix inversion
Combinatorica
NC algorithms for computing the number of perfect matchings in K3,3-free graph and related problems
Information and Computation
The design and analysis of algorithms
The design and analysis of algorithms
On the parallel complexity of Hamiltonian cycle and matching problem on dense graphs
Journal of Algorithms
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Fast parallel algorithms for graph matching problems
Fast parallel algorithms for graph matching problems
Matching and multidimensional matching in chordal and strongly chordal graphs
Discrete Applied Mathematics
The complexity of restricted spanning tree problems
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Unique maximum matching algorithms
Journal of Algorithms
NC Algorithms for Comparability Graphs, Interval Gaphs, and Testing for Unique Perfect Matching
Proceedings of the Fifth Conference on Foundations of Software Technology and Theoretical Computer Science
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
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
Planarity, Determinants, Permanents, and (Unique) Matchings
ACM Transactions on Computation Theory (TOCT)
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs
Theory of Computing Systems - Special Title: Symposium on Theoretical Aspects of Computer Science; Guest Editors: Susanne Albers, Pascal Weil
On the Matching Problem for Special Graph Classes
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
A fast parallel algorithm for routing in permutation networks
IEEE Transactions on Computers
On the bipartite unique perfect matching problem
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Algorithmica
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To reduce a graph problem to its planar version, a standard technique is to replace crossings in a drawing of the input graph by planarizing gadgets. We show unconditionally that such a reduction is not possible for the perfect matching problem and also extend this to some other problems related to perfect matching. We further show that there is no planarizing gadget for the Hamiltonian cycle problem.