High girth augmented trees are huge

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a graph consisting of a complete binary tree of depth h together with one back edge leading from each leaf to one of its ancestors, and suppose that the girth of G exceeds g. Let h=h(g) be the minimum possible depth of such a graph. The existence of such graphs, for arbitrarily large g, is proved in [2], where it is shown that h(g) is at most some version of the Ackermann function. Here we show that this is tight and the growth of h(g) is indeed Ackermannian.

Original languageEnglish
Pages (from-to)7-15
Number of pages9
JournalJournal of Combinatorial Theory - Series A
Volume144
DOIs
StatePublished - 1 Nov 2016

Keywords

  • Ackermann Hierarchy
  • Chromatic number
  • High girth

Fingerprint

Dive into the research topics of 'High girth augmented trees are huge'. Together they form a unique fingerprint.

Cite this