### Abstract

The threshold dimension of a graph G is the smallest number of threshold graphs needed to cover the edges of G. If t(n) is the greatest threshold dimension of any graph of n vertices, we show that for some constant c, n minus c n log n less than t(n) less than n minus n plus 1 We establish the same bounds for edge-disjoint coverings of graphs by threshold graphs. The results have applications to manipulating systems of simultaneous linear inequalities and to space bounds for synchronization problems.

Original language | English |
---|---|

Title of host publication | Unknown Host Publication Title |

Publisher | ACM |

Pages | 422 |

Number of pages | 1 |

ISBN (Print) | 0897911504 |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Unknown Host Publication Title*(pp. 422). ACM.

**BOUNDS ON THRESHOLD DIMENSION AND DISJOINT THRESHOLD COVERINGS.** / Erdős, P.; Ordman, E.; Zalcstein, Y.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Unknown Host Publication Title.*ACM, pp. 422.

}

TY - GEN

T1 - BOUNDS ON THRESHOLD DIMENSION AND DISJOINT THRESHOLD COVERINGS.

AU - Erdős, P.

AU - Ordman, E.

AU - Zalcstein, Y.

PY - 1985

Y1 - 1985

N2 - The threshold dimension of a graph G is the smallest number of threshold graphs needed to cover the edges of G. If t(n) is the greatest threshold dimension of any graph of n vertices, we show that for some constant c, n minus c n log n less than t(n) less than n minus n plus 1 We establish the same bounds for edge-disjoint coverings of graphs by threshold graphs. The results have applications to manipulating systems of simultaneous linear inequalities and to space bounds for synchronization problems.

AB - The threshold dimension of a graph G is the smallest number of threshold graphs needed to cover the edges of G. If t(n) is the greatest threshold dimension of any graph of n vertices, we show that for some constant c, n minus c n log n less than t(n) less than n minus n plus 1 We establish the same bounds for edge-disjoint coverings of graphs by threshold graphs. The results have applications to manipulating systems of simultaneous linear inequalities and to space bounds for synchronization problems.

UR - http://www.scopus.com/inward/record.url?scp=0022231452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022231452&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897911504

SP - 422

BT - Unknown Host Publication Title

PB - ACM

ER -