The firefighter problem on polynomial and intermediate growth groups

Gideon Amir, Rangel Baldasso, Gady Kozma

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We prove that any Cayley graph G with degree d polynomial growth does not satisfy {f(n)}-containment for any f=o(nd−2). This settles the asymptotic behaviour of the firefighter problem on such graphs as it was known that Cnd−2 firefighters are enough, answering and strengthening a conjecture of Develin and Hartke. We also prove that intermediate growth Cayley graphs do not satisfy polynomial containment, and give explicit lower bounds depending on the growth rate of the group. These bounds can be further improved when more geometric information is available, such as for Grigorchuk's group.

Original languageEnglish
Article number112077
JournalDiscrete Mathematics
Volume343
Issue number11
DOIs
StatePublished - Nov 2020

Bibliographical note

Funding Information:
The authors would like to thank all the suggestions of the anonymous referee. While performing this research, G.A. and R.B. were supported by the Israel Science Foundation grant #575/16 and by GIF grant #I-1363-304.6/2016 . G.K. was supported by the Israel Science Foundation grant #1369/15 and by the Jesselson Foundation .

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Cayley graphs
  • Firefighter problem

Fingerprint

Dive into the research topics of 'The firefighter problem on polynomial and intermediate growth groups'. Together they form a unique fingerprint.

Cite this