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Given a graph í µí°º = (í µí±‰, í µí°¸) with í µí±› vertices and í µí±š edges, and a subset í µí±‡ of í µí±˜ vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most í µí±™ edges (non-terminal vertices), whose removal from í µí°º separates each terminal from all the others. These two problems are(More)
We present an O * (1.0836 n)-time algorithm for finding a maximum independent set in an n-vertex graph with degree bounded by 3, which improves all previous running time bounds for this problem. Our approach has the following two features. Without increasing the number of reduction/branching rules to get an improved time bound, we first successfully extract(More)
The minimum 3-way cut problem in an edge-weighted hyper-graph is to find a partition of the vertices into 3 sets minimizing the total weight of hyperedges with at least two endpoints in two different sets. In this paper we present some structural properties for minimum 3-way cuts and design an O(dmn 3) algorithm for the minimum 3-way cut problem in(More)
A dominating induced matching, also called an efficient edge domination, of a graph G = (V, E) with n = |V | vertices and m = |E| edges is a subset F ⊆ E of edges in the graph such that no two edges in F share a common endpoint and each edge in E\F is incident with exactly one edge in F. It is NP-hard to decide whether a graph admits a dominating induced(More)
We present an O * (1.3160 n)-time algorithm for the edge dominating set problem in an n-vertex graph, which improves previous exact algorithms for this problem. The algorithm is analyzed by using the " Measure and Conquer method. " We design new branching rules based on conceptually simple local structures, called " clique-producing vertices/cycles, " which(More)