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))log 2 n. Thus the sum of the bandwidths of a graph and its complement is almost always at least 2n - (4 + 2√2 + o(1))log 2 n; we prove that it is always at most 2n - 4log 2 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
Publication statusPublished - 2001

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Ramsey Theory
Bandwidth
Graph in graph theory
Vertex Labeling
Labeling
Labels
Complement
Adjacent
Distinct
Integer
Vertex of a graph

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

Ramsey theory and bandwidth of graphs. / Füredi, Zoltán; West, Douglas B.

In: Graphs and Combinatorics, Vol. 17, No. 3, 2001, p. 463-471.

Research output: Contribution to journalArticle

Füredi, Z & West, DB 2001, 'Ramsey theory and bandwidth of graphs', Graphs and Combinatorics, vol. 17, no. 3, pp. 463-471.
Füredi, Zoltán ; West, Douglas B. / Ramsey theory and bandwidth of graphs. In: Graphs and Combinatorics. 2001 ; Vol. 17, No. 3. pp. 463-471.
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