Structural Parameterizations of Vertex Integrity

The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected components small. In this paper, we initiate a systematic study of structural parameterizations of the problem of computing the unweighted/weighted vertex integrity. As structural graph parameters, we consider well-known parameters such as clique-width, treewidth, pathwidth, treedepth, modular-width, neighborhood diversity, twin cover number, and cluster vertex deletion number. We show several positive and negative results and present sharp complexity contrasts.Comment: 21 pages, 6 figures, WALCOM 202

Some notes on bounded starwidth graphs

We introduce the graph parameter starwidth. We show results on characterization, complexity and the relation with other parameters. We also discuss the complexity of problems on bounded starwidth graphs

Some notes on bounded starwidth graphs

We introduce the graph parameter starwidth. We show results on characterization, complexity and the relation with other parameters. We also discuss the complexity of problems on bounded starwidth graphs