Exploring the Gap Between Treedepth and Vertex Cover Through Vertex Integrity

For intractable problems on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained complexity results. Although the studies in this direction are successful, we still need a systematic way for further investigations because form rather small subclass treedepth. To fill gap, use integrity, which is placed between mentioned above. several problems, generalize fixed-parameter tractability results parameterized by ones integrity. We also show some finer contrasts showing hardness with respect integrity or