L. Stockmeyer, and V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. Information Processing Letters, 15(1), pp. 14-19, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a proper mapping in a hypergraph can be viewed as the reason for the existence of many maximal independent sets. These reasons, however, may not be easy to exhibit for a given graph or hypergraph. The problem of finding the maximum size induced matching in a graph is known to be NPhard (see e.g. [31]) and it is even hard to approximate it well (see [15] The 7 complexities of the corresponding problems of finding or approximating well the largest binary tree with a proper mapping are open. The problem of generating all maximal independent sets for a general independence system was shown to ....

Larry J. Stockmeyer and Vijay V. Vazirani, NP-completeness of some generalizations of the maximum matching problem. Information Processing Letters, 15(1):14-19, 19 August 1982.

....a well studied problem and is proved to be NP complete even for planar graphs of bounded degree. Although there are efficient algorithms for the standard matching problem, finding a maximum induced matching (called MIM from now on) is NP complete, even for bipartite graphs with maximum degree 4 [20] and for 3 regular graphs [13] On the other hand, the MIM problem is solvable in polynomial time for trees [9] chordal graphs [6] circular arc graphs [10] trapezoid graphs, co comparability graphs [11] and weakly chordal graphs [21] The main idea of the most of these algorithms is to show ....

L.J. Stockmeyer and V.V. Vazirani, NP-completeness of some generalizations of the maximum matching problem, Inform. Proc. Letters 15(1) 1982 14-19.

....M is induced if for every edge e = fu; vg, e 2 M if and only if u; v 2 V (M) and e 2 E. Let I (G) denote the maximum cardinality of an induced matching in G. The maximum induced matching problem (MIM) is that of nding an induced matching in G with I (G) edges. The problem was introduced in [14] as a variation of the maximum matching problem and motivated as the risk free marriage problem: nd the maximum number of pairs such that each married person is compatible with no married person other than the one he (or she) is married to. Induced matchings have stimulated a lot of interest in ....

....large induced matchings is a subtask of nding a strong edge colouring in a graph (see [5, 6] and [15, 11] for more recent results) a proper colouring of the edges such that no edge is adjacent to two edges of the same colour. MIM is NP complete even for bipartite graphs of maximum degree four [14]. One way of coping with the NP completeness of an optimization problem is to relax the optimality requirement and look for the existence of polynomial time algorithms which guarantee solutions whose size is close to the size of the optimum. In what follows we say that a maximization problem P is ....

L. J. Stockmeyer and V. V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. I.P.L., 15(1):14-19, August 1982.

....simple circuit of length at least four there exists an edge not in the circuit connecting two vertices belonging to the circuit. Horton and Kilakos also gave a O(n 3 ) algorithm for classes of chordal graphs and a few other classes. Induced Matchings. The first proof of NP completeness is in [SV82]. The authors present their results in terms of separated matchings. The notion of distance between two vertices, defined in Section 1.2.4, can be extended in the obvious way to pairs of edges. Given a graph G = V; E) for all e; f 2 E the distance dst G (e; f) is the length of the shortest path ....

L. J. Stockmeyer and V. V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. Information Processing Letters, 15(1):14--19, August 1982.

.... jMj 0:2821n. 1 Introduction An induced matching of a graph G = V; E) is a set of vertex disjoint edges M E with the additional constraint that no two edges of M are connected by an edge of E n M. We are interested in finding induced matchings of large cardinality. Stockmeyer and Vazirani [10] introduced the problem of finding a maximum induced matching of a graph, motivating it as the risk free marriage problem (find the maximum number of married couples such that each person is compatible only with the person (s)he is married to) This in turn stimulated much interest in other ....

.... finding a strong edge colouring (a proper colouring of the edges such that no edge is incident with more than one edge of the same colour) of a graph (see [5, 6, 8, 9] The problem of deciding whether for a given integer k a given graph G has an induced matching of size at least k is NP Complete [10], even for bipartite graphs of maximum degree 4. Zito [12] showed that this problem remains NP Complete when restricted to 4s regular graphs for all s 1. Duckworth, Manlove and Zito [3] showed that the problem remains NP Complete even when restricted to planar cubic graphs and planar bipartite ....

L. J. Stockmeyer and V. V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. Information Processing Letters, 15(1):14--19, 1982.

.... jMj 0:2821n. 1 Introduction An induced matching of a graph G = V; E) is a set of vertex disjoint edges M E with the additional constraint that no two edges of M are connected by an edge of E n M. We are interested in nding induced matchings of large cardinality. Stockmeyer and Vazirani [11] introduced the problem of nding a maximum induced matching of a graph, motivating it as the risk free marriage problem ( nd the maximum number of married couples such that each person is compatible only with the person (s)he is married to) This in turn stimulated much interest in other areas ....

.... of a graph (a proper colouring of the edges such that no edge is incident with more than one edge of the same colour as each other, see (for example) 5, 6, 9, 10] The problem of deciding whether for a given integer k a given graph G has an induced matching of size at least k is NP Complete [11], even for bipartite graphs of maximum degree 4. It has been shown [3, 13] that the problem is APX complete even when restricted to ks regular graphs for k 2 f3; 4g and any integer s 1. The problem of nding a maximum induced matching is polynomial time solvable for chordal graphs [2] and ....

Stockmeyer, L.J. and Vazirani, V.V.: NP-Completeness of Some Generalizations of the Maximum Matching Problem. Inf. Proc. Lett., 15(1):14-19, 1982.

....a matching; M is induced if for every edge e = fu; vg, e 2 M if and only if u; v 2 V (M) and e 2 E. Let I (G) denote the maximum cardinality of an induced matching in G. The name MAXINDMATCH will identify the problem of finding the largest induced matching in G. The problem was introduced in [SV82] as a variation of the maximum matching problem and motivated as the risk free marriage problem: find the maximum number of pairs such that each married person is compatible with no married person other than the one he (or she) is married to. Induced matchings have stimulated a lot of interest ....

....is a subtask of finding a strong edge colouring in a graph (see [Erd88,FGST89] and [SY93,LZ97] for more recent results) a proper colouring of the edges such that no edge is adjacent to two edges of the same colour. MAXINDMATCH is NP complete even for bipartite graphs of maximum degree four [SV82]. No hardness result was known for regular graphs. In Section 2 we prove that the problem is NP complete for regular graphs of degree 4s for any positive integer s. One way of coping with the NP completeness of a particular optimisation problem is to relax the optimality requirement and look for ....

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L. J. Stockmeyer and V. V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. Information Processing Letters, 15(1):14--19, August 1982.

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L. Stockmeyer, and V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. Information Processing Letters, 15(1), pp. 14-19, 1982.

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