TY - JOUR

T1 - The balanced connected subgraph problem

AU - Bhore, Sujoy

AU - Chakraborty, Sourav

AU - Jana, Satyabrata

AU - Mitchell, Joseph S.B.

AU - Pandit, Supantha

AU - Roy, Sasanka

N1 - Funding Information:
Support from the National Science Foundation, USA (CCF-1526406) and the US-Israel Binational Science Foundation (project 2016116).This work was done while the author was at the Stony Brook University, Stony Brook, NY, USA and was partially supported by the Indo-US Science & Technology Forum (IUSSTF) under the SERB Indo-US Postdoctoral Fellowship scheme with grant number 2017/94, Department of Science and Technology, Government of India.
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2022/10/15

Y1 - 2022/10/15

N2 - The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following [Formula presented] ( [Formula presented] ) problem. The input is a graph G=(V,E), with each vertex in the set V having an assigned color, “ [Formula presented] ” or “ [Formula presented] ”. We seek a maximum-cardinality subset V′⊆V of vertices that is [Formula presented] (having exactly |V′|/2 red vertices and |V′|/2 blue vertices), such that the subgraph induced by the vertex set V′ in G is connected. We show that the BCS problem is NP-hard, even for bipartite graphs G (with red/blue color assignment not necessarily being a proper 2-coloring). Further, we consider this problem on various graph classes, e.g., planar graphs, chordal graphs, trees, split graphs, bipartite graphs with a proper red/blue 2-coloring, and graphs with diameter 2. For each of these classes we either prove NP-hardness or design a polynomial time algorithm.

AB - The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following [Formula presented] ( [Formula presented] ) problem. The input is a graph G=(V,E), with each vertex in the set V having an assigned color, “ [Formula presented] ” or “ [Formula presented] ”. We seek a maximum-cardinality subset V′⊆V of vertices that is [Formula presented] (having exactly |V′|/2 red vertices and |V′|/2 blue vertices), such that the subgraph induced by the vertex set V′ in G is connected. We show that the BCS problem is NP-hard, even for bipartite graphs G (with red/blue color assignment not necessarily being a proper 2-coloring). Further, we consider this problem on various graph classes, e.g., planar graphs, chordal graphs, trees, split graphs, bipartite graphs with a proper red/blue 2-coloring, and graphs with diameter 2. For each of these classes we either prove NP-hardness or design a polynomial time algorithm.

KW - Balanced connected subgraph

KW - Bipartite graphs

KW - Chordal graphs

KW - NP-hard

KW - Planar graphs

KW - Polynomial algorithms

KW - Split graphs

KW - Trees

UR - http://www.scopus.com/inward/record.url?scp=85099821646&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2020.12.030

DO - 10.1016/j.dam.2020.12.030

M3 - Article

AN - SCOPUS:85099821646

SN - 0166-218X

VL - 319

SP - 111

EP - 120

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -