The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some n...
We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an exp...
Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wishes to partition G into connected components by del...
For a real c 1 and an integer n, let f(n, c) denote the maximum integer f such that every graph on n vertices contains an induced subgraph on at least f vertices in which the max...