Maximum h-Colourable Subgraph Problem in Balanced Graphs

The k-fold clique transversal problem is to locate a minimum set of vertices of a graph such that every maximal clique has at least k elements of. The maximum h-colourable subgraph problem is to nd a maximum subgraph of a graph which is h-colourable. We show that the k-fold clique transversal problem and the maximum h-colourable subgraph problem are polynomially solvable on balanced graphs. We also provide a polynomial algorithm to recognize balanced graphs. matrix, k-fold clique transversal problem, maximum h-colourable subgraph problem.