Linear-time computation of optimal subgraphs of decomposable graphs
Journal of Algorithms
Gallai theorems for graphs, hypergraphs, and set systems
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
On generalised minimal domination parameters for paths
Discrete Mathematics - Topics on domination
Approximating matchings in parallel
Information Processing Letters
A separation algorithm for the matchable set polytope
Mathematical Programming: Series A and B
Regularity and locality in k-terminal graphs
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Approximate Max-Flow on Small Depth Networks
SIAM Journal on Computing
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
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We present a collection of new structural, algorithmic, and complexity results for matching problems of two types. The first problem involves the computation of k-maximal matchings, where a matching is k-maximal if it admits no augmenting path with @?2k vertices. The second involves finding a maximal set of vertices that is matchable - comprising one side of the edges in some matching. Among our results, we prove that the minimum cardinality @b"2 of a 2-maximal matching is at most the minimum cardinality @m of a maximal matchable set, with equality attained for triangle-free graphs. We show that the parameters @b"2 and @m are NP-hard to compute in bipartite and chordal graphs, but can be computed in linear time on a tree. Finally, we also give a simple linear-time algorithm for finding a 3-maximal matching, a consequence of which is a simple linear-time 3/4-approximation algorithm for the maximum-cardinality matching problem in a general graph.