On the maximum connected interval subgraph of block grraphs and chain graphs

Abstract

The maximum connected interval subgraph problem on a graph G is the problem of nding an induced subgraph H of G such that H is a connected interval graph with the maximum number of vertices. It has been shown that this problem is NP-hard and have no constant ratio approximation on general graphs. In this paper, we propose linear-time algorithms for solving this problem on block graphs and chain graphs.