The maximum happy induced subgraph problem: Bounds and algorithms

In this paper we consider a combinatorial optimisation problem that takes as input graph in which some of the vertices have been preassigned to colours. The aim is then identify largest induced subgraph all remaining are able assume same colour their neighbours. This shares similarities with colouring problem, vertex cut problems, and maximum happy problem. It NP-hard general. derive number upper lower bounds also show how certain instances can be broken up into smaller subproblems. We propose one exact two heuristic algorithms for use these investigate factors make more difficult solve than others.