Radius three trees in graphs with large chromatic number

Henry Kierstead, Yingxian Zhu

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A class γ of graphs is χ-bounded if there exists a function f such that χ (G) ≤ f (ω (G)) for all graphs G ∈ γ, where χ denotes chromatic number and ω denotes clique number. Gyárfás and Sumner independently conjectured that, for any tree T, the class Forb (T), consisting of graphs that do not contain T as an induced subgraph, is χ-bounded. The first author and Penrice showed that this conjecture is true for any radius two tree. Here we use the work of several authors to show that the conjecture is true for radius three trees obtained from radius two trees by making exactly one subdivision in every edge adjacent to the root. These are the only trees with radius greater than two, other than subdivided stars, for which the conjecture is known to be true.

Original languageEnglish (US)
Pages (from-to)571-581
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Volume17
Issue number4
DOIs
StatePublished - Apr 2004

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Chromatic number
Stars
Radius
Graph in graph theory
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Clique number
Induced Subgraph
Subdivision
Star
Adjacent
Roots
Class

Keywords

  • Chromatic number
  • Clique number
  • Forbidden induced subgraph
  • Radius three tree
  • Template

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Radius three trees in graphs with large chromatic number. / Kierstead, Henry; Zhu, Yingxian.

In: SIAM Journal on Discrete Mathematics, Vol. 17, No. 4, 04.2004, p. 571-581.

Research output: Contribution to journalArticle

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