Ramsey theory and bandwidth of graphs

Zoltán Füredi, Douglas B. West

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The bandwidth of a graph is the minimum, over vertex labelings with distinct integers, of the maximum difference between labels on adjacent vertices. Kuang and McDiarmid proved that almost all n-vertex graphs have bandwidth n - (2 + √2 + o(1))log2 n. Thus the sum of the bandwidths of a graph and its complement is almost always at least 2n - (4 + 2√2 + o(1))log2 n; we prove that it is always at most 2n - 4log2 n + o(log n). The proofs involve improving the bounds on the Ramsey and Turán numbers of the "halfgraph".

Original languageEnglish
Pages (from-to)463-471
Number of pages9
JournalGraphs and Combinatorics
Volume17
Issue number3
DOIs
Publication statusPublished - Jan 1 2001

Keywords

  • Bandwidth
  • Halfgraph
  • Ramsey number
  • Random graph
  • Turán number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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