Domination properties and induced subgraphs

G. Bascó, Z. Tuza

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let the class Forb(Ct, Pt) consist of all graphs containing no induced cycle or path on t vertices, and denote by Dom(d, k) the class of graphs in which every connected induced subgraph H has a k-dominating subgraph D of diameter at most d (i.e. for each vertex x ε{lunate} V(H) {minus 45 degree rule} V(D), there is a vertex y ε{lunate} V(D) at distance ≤k from x). In a previous paper we proved Forb(Ct, Pt) = Dom(t-4, 1) for 4≤t≤6 and Forb(Pt) = Dom(t-4, 1) for t≥7. Here we show Forb(Ct, Pt⊆Dom(t-6, 2) for t≥9; moreover, Forb(C9, P9) = Dom(3, 2) and Forb(C10, P10) = Dom(4, 2).

Original languageEnglish
Pages (from-to)37-40
Number of pages4
JournalDiscrete Mathematics
Volume111
Issue number1-3
DOIs
Publication statusPublished - Feb 22 1993

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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