M. Golumbic, and M. Lewenstein. New Results on Induced Matchings. Discrete Applied Math., 101:157-165, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... (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 that for a class C of graphs, if G 2 C then L(G) 2 C as well. This immediately yields a polynomial time algorithm for the MIM problem, because an induced matching of G is equivalent to an independent set ....

M.C. Golumbic and M. Lewenstein, New results on induced matchings, Disc. Appl. Math. 101 (2000) 157-165.

....G is denoted RRR 9 2001 Page 7 i(G) The problem of finding a maximum induced matching has been introduced in [3] where the author proved its NP hardness in the class of bipartite graphs. On the other hand, the problem is known to be solvable in the class of trees in linear time [6, 11] see [7] for more solvable cases for the problem) Below we use the solution for trees in order to develop an efficient procedure to solve the problem in the class of (S 2;2;2 ; A) free bipartite graphs. Again, like for the jump number problem, it is obviously sufficient to consider only connected ....

M.C. Golumbic and M. Lewenstein, New results on induced matchings, Discrete Applied Mathematics, 101 (2000) 157-165.

....to be NP complete for general bipartite graphs. Paper [24] strengthens the result by reducing the problem to some special classes of bipartite graphs such as bipartite graphs with maximum degree 3 or C 4 free bipartite graphs. There are known several polynomially solvable cases for this problem [5, 11, 17, 18, 24]. The result in [24] deals with a generalization of bi complement reducible graphs [22] which is a subclass of bipartite graphs without a skew star. We hope to use the relationship between classes to extend the polynomial solvability RRR 20 2001 Page 17 of the problem from the smaller class to ....

M.C. Golumbic and M. Lewenstein, New results on induced matchings, Discrete Applied Mathematics, 101 (2000) 157-165.

.... maximum independent set in the square of the line graph of G (see [2] For many classes of graphs (e.g. chordal graphs, circular arc graphs, co comparability graphs, and trapezoid graphs) it is proved that if a graph G is in the class C, then the square of the line graph of G is also in C (see [2, 9]) Therefore, if we can solve the maximum independent set problem in class C, we can also solve the induced matching problem in this class. The same idea can be applied to the strong edge coloring problem, because a strong edge coloring of a graph G is a proper vertex coloring of the square of ....

....be applied to the strong edge coloring problem, because a strong edge coloring of a graph G is a proper vertex coloring of the square of the line graph of G. Using this fact, we can obtain polynomial time algorithms for strong edge coloring of chordal graphs (see [2] and co comparability graphs ([9] and [7] The latter class contains interval graphs, permutation graphs, and trapezoid graphs. Also, we can get a 1.368 approximation algorithm for circular arc graphs ( 8] and [11] Similarly, since the maximum antimatching in a graph corresponds to the maximum clique in the square of its line ....

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M. C. Golumbic, and M. Lewenstein, New results on induced matchings, Discrete Applied Mathematics 101 (2000), 157-165.

.... graphs [8] An earlier version of this paper appeared in the proceedings of COCOON 2000 y Currently in the Department of Computing, Macquarie University, Australia z Supported by the Australian Research Council x Supported by EPSRC grant GR L 77089 1 Recently, Golumbic and Lewenstein [9] have constructed polynomial time algorithms for maximum induced matching in trapezoid graphs, interval dimension graphs and co comparability graphs and have given a linear time algorithm for maximum induced matching in interval graphs. In this paper, we present a heuristic for nding a large ....

Golumbic, M.C. and Lewenstein, M.: New Results on Induced Matchings. Discrete Applied Mathematics, 101:157-165, 2000.

....each vertex in one partite set has degree 2 and each vertex in the other partite set has degree at most 3. 1 Cameron (1989) shows that MIM is solvable in polynomial time for chordal graphs, and Golumbic and Laskar (1993) give a polynomialtime algorithm for MIM in circular arc graphs. Recently Golumbic and Lewenstein (2000) have constructed polynomial time algorithms for MIM in trapezoid graphs, interval dimension graphs and cocomparability graphs, and have given a linear time algorithm for MIM in interval graphs. Fricke and Laskar (1992) give a linear time algorithm for MIM in trees. Independently, Zito (1999) and ....

....have constructed polynomial time algorithms for MIM in trapezoid graphs, interval dimension graphs and cocomparability graphs, and have given a linear time algorithm for MIM in interval graphs. Fricke and Laskar (1992) give a linear time algorithm for MIM in trees. Independently, Zito (1999) and Golumbic and Lewenstein (2000), have given simpler linear time algorithms for MIM in trees. Note that in Fricke and Laskar, 1992; Golumbic and Laskar, 1993, induced matchings are referred to as as strong matchings. Regarding the approximability of MIM, Zito (1999) has shown that for every k 1, there is a constant c 1 such ....

Golumbic, M. and M. Lewenstein: 2000, `New results on induced matchings'. Discrete Applied Mathematics 101, 157--165.

.... 1. The problem of nding a maximum induced matching is polynomial time solvable for chordal graphs [2] and circular arc graphs [7] Supported by the Australian Research Council Supported by EPSRC grant GR L 77089 2 W. Duckworth, N.C. Wormald and M. Zito Recently Golumbic and Lewenstein [8] have constructed polynomial time algorithms for maximum induced matching in trapezoid graphs, interval dimension graphs and co comparability graphs, and have given a linear time algorithm for maximum induced matching in interval graphs. In this paper we present a heuristic for nding a large ....

Golumbic, M.C. and Lewenstein, M.: New Results on Induced Matchings. Discrete Applied Math., 101:157-165, 2000.

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M. Golumbic, and M. Lewenstein. New Results on Induced Matchings. Discrete Applied Math., 101:157-165, 2000.

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M. C. Golumbic and M. Lewenstein. New results in induced matchings. Discrete Applied Mathematics, 101(1-3):157--165, 2000. 8

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