Cycle-saturated graphs with minimum number of edges

Zoltán Füredi, Younjin Kim

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A graph G is called H-saturated if it does not contain any copy of H, but for any edge e in the complement of G, the graph G+e contains some H. The minimum size of an n-vertex H-saturated graph is denoted by sat(n,H). We prove sat(n,Ck)=n+n/k+O((n/k2)+k2)holds for all n≥k≥3, where Ck is a cycle with length k. A graph G is H-semisaturated if G+e contains more copies of H than G does for â̂€eâ̂̂E(Ḡ). Let ssat (n,H) be the minimum size of an n-vertex H-semisaturated graph. We have ssat(n,Ck)=n+n/(2k)+O((n/k2)+k).We conjecture that our constructions are optimal for n>n0(k).

Original languageEnglish
Pages (from-to)203-215
Number of pages13
JournalJournal of Graph Theory
Volume73
Issue number2
DOIs
Publication statusPublished - Jun 2013

Keywords

  • cycles
  • extremal graphs
  • graphs
  • minimal saturated graphs

ASJC Scopus subject areas

  • Geometry and Topology

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