Author:
Gurski Frank,Rothe Jörg,Weishaupt Robin
Abstract
AbstractFrei et al. (J. Comput. Syst. Sci. 123, 103–121, 2022) show that the stability, vertex stability, and unfrozenness problems with respect to certain graph parameters are complete for $$\varvec{\Theta _{2}^{\textrm{P}}}$$
Θ
2
P
, the class of problems solvable in polynomial time by parallel access to an NP oracle. They studied the common graph parameters $$\varvec{\alpha }$$
α
(the independence number), $$\varvec{\beta }$$
β
(the vertex cover number), $$\varvec{\omega }$$
ω
(the clique number), and $$\varvec{\chi }$$
χ
(the chromatic number). We complement their approach by providing polynomial-time algorithms solving these problems for special graph classes, namely for graphs with bounded tree-width or bounded clique-width. In order to improve these general time bounds even further, we then focus on trees, forests, bipartite graphs, and co-graphs.
Funder
Heinrich-Heine-Universität Düsseldorf
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Theoretical Computer Science