### Abstract

We give counter-examples to the following conjecture which arose in the study of small bandwidth graphs. “For a graph G, suppose that |V(G')|≤ 1 + c_{1} diameter (G') for any connected subgraph G' of G, and that G does not contain any refinement of the complete binary tree of c_{2} levels. Is it true that the bandwidth of G can be bounded above by a constant c depending only on c_{1}and c_{2}?” On the other hand, we show that if the maximum degree of G is bounded and G does not contain any refinement of a complete binary tree of a specified size, then the cutwidth and the topological bandwidth of G are also bounded.

Original language | English (US) |
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Pages (from-to) | 113-119 |

Number of pages | 7 |

Journal | Annals of Discrete Mathematics |

Volume | 43 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1989 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Graphs with Small Bandwidth and Cutwidth'. Together they form a unique fingerprint.

## Cite this

Chung, F. R. K., & Seymour, P. D. (1989). Graphs with Small Bandwidth and Cutwidth.

*Annals of Discrete Mathematics*,*43*(C), 113-119. https://doi.org/10.1016/S0167-5060(08)70571-5