Minimum Maximal Matching Is NP-Hard in Regular Bipartite Graphs
نویسندگان
چکیده
Yannakakis and Gavril showed in [10] that the problem of finding a maximal matching of minimum size (MMM for short), also called Minimum Edge Dominating Set, is NP-hard in bipartite graphs of maximum degree 3 or planar graphs of maximum degree 3. Horton and Kilakos extended this result to planar bipartite graphs and planar cubic graphs [6]. Here, we extend the result of Yannakakis and Gavril in [10] by showing that MMM is NP-hard in the class of k-regular bipartite graphs for all k ≥ 3 fixed.
منابع مشابه
Approximability results for the maximum and minimum maximal induced matching problems
An induced matching M of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M . The MINIMUM MAXIMAL INDUCED MATCHING problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complete. Here we show that, if P 6= NP, for any ε >...
متن کاملComplexity results for minimum sum edge coloring
In the Minimum Sum Edge Coloring problem we have to assign positive integers to the edges of a graph such that adjacent edges receive different integers and the sum of the assigned numbers is minimal. We show that the problem is (a) NP-hard for planar bipartite graphs with maximum degree 3, (b) NP-hard for 3-regular planar graphs, (c) NP-hard for partial 2-trees, and (d) APX-hard for bipartite ...
متن کاملThe Complexity of Counting in Sparse, Regular, and Planar Graphs
We show that a number of graph-theoretic counting problems remain NP-hard, indeed #P-complete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree. To achieve these ...
متن کاملMatchability and k-maximal matchings
We present a collection of new structural, algorithmic, and complexity results for two types of matching problems. 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 ou...
متن کاملOn Minimum Feedback Vertex Sets in Bipartite Graphs and Degree-Constraint Graphs
We consider the minimum feedback vertex set problem for some bipartite graphs and degree-constrained graphs. We show that the problem is linear time solvable for bipartite permutation graphs and NP-hard for grid intersection graphs. We also show that the problem is solvable in O(n2 log6 n) time for n-vertex graphs with maximum degree at most three. key words: 3-regular graph, bipartite permutat...
متن کامل