Constrained minimum vertex cover in bipartite graphs: complexity and parameterized algorithms

Minimum Degree Up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms

The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted to bipartite graphs. Regarding the upper bound, we show that for any graph of order n, its local minimum degree is at most 3 8 n + o(n) and n 4 + o(n) for bi...

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism

Maximum Common Induced Subgraph (henceforth MCIS) is among the most studied classical NP-hard problems. MCIS remains NP-hard on many graph classes including bipartite graphs, planar graphs and k-trees. Little is known, however, about the parameterized complexity of the problem. When parameterized by the vertex cover number of the input graphs, the problem was recently shown to be fixed-paramete...

On Constrained Minimum Vertex Covers of Bipartite Graphs: Improved Algorithms

Vertex Cover Reconfiguration and Beyond

In the Vertex Cover Reconfiguration (VCR) problem, given graph G = (V,E), positive integers k and `, and two vertex covers S and T of G of size at most k, we determine whether S can be transformed into T by a sequence of at most ` vertex additions or removals such that each operation results in a vertex cover of size at most k. Motivated by recent results establishing the W[1]-hardness of VCR w...

On Covering Points with Minimum Turns

For the rectilinear version of the problem in which the lines must be axis-parallel, • Hassin and Megiddo (1991) observed that the problem in R reduces to vertex cover in bipartite graphs and hence is solvable in polynomial time, and proved that the problem in R in NP-hard by a reduction from 3SAT, • Gaur and Bhattacharya (2007) presented a (d − 1)approximation algorithm for the problem in R fo...