The Balanced Connected Subgraph Problem

  • Sujoy Bhore
  • Sourav Chakraborty
  • Satyabrata Jana
  • Joseph S. B. Mitchell
  • Supantha PanditEmail author
  • Sasanka Roy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)


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 Open image in new window (shortly, Open image in new window ) problem. The input is a graph \(G=(V,E)\), with each vertex in the set V having an assigned color, “ Open image in new window ” or “ Open image in new window ”. We seek a maximum-cardinality subset \(V'\subseteq V\) of vertices that is Open image in new window (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.


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



We thank Florian Sikora for pointing out the connection with the Graph Motif problem.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sujoy Bhore
    • 1
  • Sourav Chakraborty
    • 2
  • Satyabrata Jana
    • 2
  • Joseph S. B. Mitchell
    • 3
  • Supantha Pandit
    • 3
    Email author
  • Sasanka Roy
    • 2
  1. 1.Ben-Gurion UniversityBeer-ShevaIsrael
  2. 2.Indian Statistical InstituteKolkataIndia
  3. 3.Stony Brook UniversityStony BrookUSA

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