Substitution and χ-boundedness

Maria Chudnovsky, Irena Penev, Alex Scott, Nicolas Trotignon

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

A class G of graphs is said to be χ. bounded if there is a function f:N→R such that for all G∈G and all induced subgraphs H of G, χ(H). ≤. f(ω(H)). In this paper, we show that if G is a χ-bounded class, then so is the closure of G under any one of the following three operations: substitution, gluing along a clique, and gluing along a bounded number of vertices. Furthermore, if G is χ-bounded by a polynomial (respectively: exponential) function, then the closure of G under substitution is also χ-bounded by some polynomial (respectively: exponential) function. In addition, we show that if G is a χ-bounded class, then the closure of G under the operations of gluing along a clique and gluing along a bounded number of vertices together is also χ-bounded, as is the closure of G under the operations of substitution and gluing along a clique together.

Original languageEnglish (US)
Pages (from-to)567-586
Number of pages20
JournalJournal of Combinatorial Theory. Series B
Volume103
Issue number5
DOIs
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Coloring
  • Connectivity
  • Graph operations
  • Homogeneous set
  • Substitution
  • χ-bounded

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