Cops, robbers, and threatening skeletons: Padded decomposition for minor-free graphs

Ittai Abraham, Cyril Gavoille, Anupam Gupta, Ofer Neiman, Kunal Talwar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

19 Scopus citations

Abstract

We prove that any graph excluding Kr as a minor has can be partitioned into clusters of diameter at most Δ while removing at most O(r/Δ) fraction of the edges. This improves over the results of Fakcharoenphol and Talwar, who building on the work of Klein, Plotkin and Rao gave a partitioning that required to remove O(r2/Δ) fraction of the edges. Our result is obtained by a new approach that relates the topological properties (excluding a minor) of a graph to its geometric properties (the induced shortest path metric). Specifically, we show that techniques used by Andreae in his investigation of the cops and robbers game on graphs excluding a fixed minor, can be used to construct padded decompositions of the metrics induced by such graphs. In particular, we get probabilistic partitions with padding parameter O(r) and strong-diameter partitions with padding parameter O(r2) for Kr-free graphs, O(κ) for treewidth-κ graphs, and O(log g) for graphs with genus g.

Original languageEnglish
Title of host publicationSTOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages79-88
Number of pages10
ISBN (Print)9781450327107
DOIs
StatePublished - 1 Jan 2014
Event4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States
Duration: 31 May 20143 Jun 2014

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference4th Annual ACM Symposium on Theory of Computing, STOC 2014
Country/TerritoryUnited States
CityNew York, NY
Period31/05/143/06/14

Keywords

  • Cops and robbers
  • Excluded minor
  • Padded decomposition

Fingerprint

Dive into the research topics of 'Cops, robbers, and threatening skeletons: Padded decomposition for minor-free graphs'. Together they form a unique fingerprint.

Cite this