DeepAI

Minimum Connected Transversals in Graphs: New Hardness Results and Tractable Cases Using the Price of Connectivity

We perform a systematic study in the computational complexity of the connected variant of three related transversal problems: Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. Just like their original counterparts, these variants are NP-complete for general graphs. A graph G is H-free for some graph H if G contains no induced subgraph isomorphic to H. It is known that Connected Vertex Cover is NP-complete even for H-free graphs if H contains a claw or a cycle. We show that the two other connected variants also remain NP-complete if H contains a cycle or claw. In the remaining case H is a linear forest. We show that Connected Vertex Cover, Connected Feedback Vertex Set, and Connected Odd Cycle Transversal are polynomial-time solvable for sP_2-free graphs for every constant s≥ 1. For proving these results we use known results on the price of connectivity for vertex cover, feedback vertex set, and odd cycle transversal. This is the first application of the price of connectivity that results in polynomial-time algorithms.

• 4 publications
• 1 publication
• 33 publications
• 25 publications
• 54 publications
08/01/2019

On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest

A graph is H-free if it contains no induced subgraph isomorphic to H. We...
10/11/2019

On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal

Let vc(G), fvs(G) and oct(G), respectively, denote the size of a minimum...
12/22/2017

Connected Vertex Cover for (sP_1+P_5)-Free Graphs

The Connected Vertex Cover problem is to decide if a graph G has a verte...
02/07/2019

Going Far From Degeneracy

An undirected graph G is d-degenerate if every subgraph of G has a verte...
09/16/2019

The Computational Complexity of Fire Emblem Series and similar Tactical Role-Playing Games

Fire Emblem (FE) is a popular turn-based tactical role-playing game (TRP...
09/04/2019

Gerrymandering: A Briber's Perspective

We initiate the study of bribery problem in the context of gerrymanderin...
09/02/2022

On the Complexity of Robust Multi-Stage Problems in the Polynomial Hierarchy

We study the computational complexity of multi-stage robust optimization...