Complexity And Inapproximability Results For Balanced Connected Subgraph Problem

This work is devoted to the study of the BALANCED CONNECTED SUBGRAPH Problem (BCS) from a complexity, inapproximability and approximation point of view. The input is a graph G = (V, E), with each vertex having been colored, "red" or "blue"; the goal is to find a maximum connected subgraph G' = (V', E') from G that is color-balanced (having exactly vertical bar V'vertical bar/2 red vertices and vertical bar V'vertical bar/2 blue vertices). This problem is known to be NP-complete in general but polynomial in paths and trees. We propose a polynomial-time algorithm for block graph. We propose some complexity results for bounded-degree or bounded-diameter graphs, and also for bipartite graphs. We also propose inapproximability results for some graph classes, including chordal, planar, or subcubic graphs. (C) 2021 Elsevier B.V. All rights reserved.