### 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 language | English |
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Pages (from-to) | 463-471 |

Number of pages | 9 |

Journal | Graphs and Combinatorics |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - 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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## Cite this

Füredi, Z., & West, D. B. (2001). Ramsey theory and bandwidth of graphs.

*Graphs and Combinatorics*,*17*(3), 463-471. https://doi.org/10.1007/PL00013410