## Partitioning Graphs with Costs and Weights on Vertices: Algorithms and Applications (0)

Venue: | of Lecture Notes in Computer Science |

Citations: | 4 - 0 self |

### BibTeX

@INPROCEEDINGS{Djidjev_partitioninggraphs,

author = {Hristo N. Djidjev},

title = {Partitioning Graphs with Costs and Weights on Vertices: Algorithms and Applications},

booktitle = {of Lecture Notes in Computer Science},

year = {},

pages = {130--143},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

We prove separator theorems in which the size of the separator is minimized with respect to non-negative vertex costs. We show that for any planar graph G there exists a vertex separator of total vertex cost at most c qP v2V (G) (cost(v)) 2 and that this bound is optimal within a constant factor. Moreover such a separator can be found in linear time. This theorem implies a variety of other separation results discussed in the paper. We describe application of our separator theorems to graph embedding problems, graph pebbling, and multi-- commodity flow problems. 1 Introduction Background. A separator is a small set of vertices or edges whose removal divides a graph into two roughly equal parts. The existence of small separators for some important classes of graphs such as planar graphs can be used in the design of efficient divide-and-conquer algorithms for problems on such graphs. Formally, a separator theorem for a given class of graphs S states that any n-vertex graph from S ca...