On the hardness of the Balanced Connected Subgraph Problem for families of Regular Graphs

Authors

Harsharaj Pathak, Indian Institute of Technology HyderabadFollow

Abstract

The Balanced Connected Subgraph problem (BCS) was introduced by Bhore et al. In the BCS problem we are given a vertex-colored graph G = (V, E) where each vertex is colored “red” or “blue”. The goal is to find a maximum cardinality induced connected subgraph H of G such that H contains an equal number of red and blue vertices. This problem is known to be NP-hard for general graphs as well as many special classes of graphs. In this work we explore the time complexity of the BCS problem in case of regular graphs. We prove that the BCS problem is NP-hard for d-regular graphs ∀d ∈ N, d > 3. We further propose a parameterized variant of the BCS problem and explore its time complexity.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Pathak, Harsharaj (2023) "On the hardness of the Balanced Connected Subgraph Problem for families of Regular Graphs," Theory and Applications of Graphs: Vol. 10: Iss. 2, Article 2.
DOI: 10.20429/tag.2023.10202
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss2/2