SIAM Journal on Discrete Mathematics
Some Matching Problems for Bipartite Graphs
Journal of the ACM (JACM)
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Approximations of Independent Sets in Graphs
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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
Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems
Algorithmica - Parameterized and Exact Algorithms
Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey
Graphs and Combinatorics
Large rainbow matchings in edge-coloured graphs
Combinatorics, Probability and Computing
Parameterized Complexity
Hi-index | 5.23 |
A rainbow matching in an edge-colored graph is a matching whose edges have distinct colors. We address the complexity issue of the following problem, max rainbow matching: Given an edge-colored graph G, how large is the largest rainbow matching in G? We present several sharp contrasts in the complexity of this problem. We show, among others, that*max rainbow matching can be approximated by a polynomial algorithm with approximation ratio 2/3-@e. *max rainbow matching is APX-complete, even when restricted to properly edge-colored linear forests without a 5-vertex path, and is solvable in polynomial time for edge-colored forests without a 4-vertex path. *max rainbow matching is APX-complete, even when restricted to properly edge-colored trees without an 8-vertex path, and is solvable in polynomial time for edge-colored trees without a 7-vertex path. *max rainbow matching is APX-complete, even when restricted to properly edge-colored paths. These results provide a dichotomy theorem for the complexity of the problem on forests and trees in terms of forbidding paths. The latter is somewhat surprising, since, to the best of our knowledge, no (unweighted) graph problem prior to our result is known to be NP-hard for simple paths. We also address the parameterized complexity of the problem.