### 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 |
---|---|

Pages (from-to) | 463-471 |

Number of pages | 9 |

Journal | Graphs and Combinatorics |

Volume | 17 |

Issue number | 3 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Bandwidth
- Halfgraph
- Ramsey number
- Random graph
- Turán number

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics

### Cite this

*Graphs and Combinatorics*,

*17*(3), 463-471.

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

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 17, no. 3, pp. 463-471.

}

TY - JOUR

T1 - Ramsey theory and bandwidth of graphs

AU - Füredi, Zoltán

AU - West, Douglas B.

PY - 2001

Y1 - 2001

N2 - 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".

AB - 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".

KW - Bandwidth

KW - Halfgraph

KW - Ramsey number

KW - Random graph

KW - Turán number

UR - http://www.scopus.com/inward/record.url?scp=19544383798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=19544383798&partnerID=8YFLogxK

M3 - Article

VL - 17

SP - 463

EP - 471

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 3

ER -