Algorithms for maximum internal spanning tree problem for some graph classes

For a given graph G, maximum internal spanning tree of G is with number vertices. The Maximum Internal Spanning Tree (MIST) problem to find the graph. MIST generalization Hamiltonian path problem. Since NP-hard, even for bipartite and chordal graphs, two important subclasses also remains NP-hard these classes. In this paper, we propose linear-time algorithms compute cographs, block cactus chain graphs permutation graphs. optimal cover problem, which asks edges, well studied study relationship between vertices in edges special classes mentioned above.