Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs

Let G be a graph with vertex set V(G) and edge set E(G). A subset D of V(G) is a dominating set of G if every vertex not in D is adjacent to one vertex of D. A dominating set is called independent if it is an independent set. The domination number ...$$${}_{\mathrm{}}$$$${}_{\mathrm{}}$${}_{}$${}_{\mathrm{}}{}_{}$${}_{}$

Efficient decomposition algorithms for the weighted maximum independent set, minimum coloring, and minimum clique cover problems on planar perfect graphs are presented. These planar graphs can also be characterized by the absence of induced odd cycles ...

The paper studies a generalization of the Independent Set problem (IS for short). A distance- $$d$$ independent set for an integer $$d\ge 2$$ in an unweighted graph $$G = (V, E)$$ is a subset $$S\subseteq V$$ of vertices such that for any pair of vertices $$u, v \in S$$ , the distance between $$u$$ and $$v$$ is at least $$d$$ ...