In a finite undirected graph G = (V,E), a vertex v ∈ V dominates itself and its neighbors. A vertex set D ⊆ V in G is an efficient dominating set (e.d. for short) of G if every vertex of G is dominated by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d. in G, is known to be NP-complete for P7-free graphs but solvable in polynomial time for ...

We initiate a general study of what we call orientation completion problems. For a fixed class C of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in C by orienting the (non-oriented) edges in P . Orientation completion problems commonly generalize several existing problems including recognition of certai...

Given an undirected graph and pairs of terminals theRestricted Vertex Multicut problem asks for a minimum set of nonterminal vertices whose removal disconnects each pair of terminals. The problem is known to be NP-complete for trees and polynomial-time solvable for interval graphs. In this paper we give a polynomial-time algorithm for the problem on permutation graphs. Furthermore we show that ...

Strictly Chordality-k graphs (SCk) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For k ≥ 5, the study has been recently initiated in [1] and various structural and algorithmic results are reported. In this paper, we show that ma...

An induced matching in a graph G is a set of edges, no two of which meet a common node or are joined by an edge of G; that is, an induced matching is a matching which forms an induced subgraph. Induced matchings in graph G correspond precisely to independent sets of nodes in the square of the line-graph of G, which we denote by [L(G)]. Often, if G has a nice representation as an intersection gr...

We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this al...

We study the node-deletion problem consisting of finding a maximum weighted induced bipartite subgraph of a planar graph with maximum degree three. We show that this is polynomially solvable. It was shown in [4] that it is NP-complete if the maximum degree is four. We also extend these ideas to the problem of balancing signed graphs. We also consider maximum weighted induced acyclic subgraphs o...

We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this al...