The balanced connected subgraph problem

Sujoy Bhore, Sourav Chakraborty, Satyabrata Jana, Joseph S.B. Mitchell, Supantha Pandit, Sasanka Roy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations


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 Balanced Connected Subgraph (shortly, BCS) problem. The input is a graph G = (V, E), with each vertex in the set V having an assigned color, "red" or "blue". We seek a maximum-cardinality subset (Formula presented) of vertices that is color-balanced (having exactly |V′|/2 red nodes and |V′|/2 blue nodes), 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 for various classes of the input graph G, including, 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 either we prove NP-hardness or design a polynomial time algorithm.

Original languageEnglish
Title of host publicationAlgorithms and Discrete Applied Mathematics - 5th International Conference, CALDAM 2019, Proceedings
EditorsAmbat Vijayakumar, Sudebkumar Prasant Pal
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783030115081
StatePublished - 1 Jan 2019
Event5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019 - Kharagpur, India
Duration: 14 Feb 201916 Feb 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11394 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019


  • Balanced connected subgraph
  • Bipartite graphs
  • Chordal graphs
  • Color-balanced
  • NP-hard
  • Planar graphs
  • Split graphs
  • Trees

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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