### Abstract

Let G be a graph on n vertices and let α and β be real numbers, 0 <α, β <1. Further, let G satisfy the condition that each ⌊αn⌋ subset of its vertex set spans at least βn^{2} edges. The following question is considered. For a fixed α what is the smallest value of β such that G contains a triangle?

Original language | English |
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Pages (from-to) | 153-161 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 127 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Mar 15 1994 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*127*(1-3), 153-161. https://doi.org/10.1016/0012-365X(92)00474-6

**A local density condition for triangles.** / Erdős, P.; Faudree, R. J.; Rousseau, C. C.; Schelp, R. H.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 127, no. 1-3, pp. 153-161. https://doi.org/10.1016/0012-365X(92)00474-6

}

TY - JOUR

T1 - A local density condition for triangles

AU - Erdős, P.

AU - Faudree, R. J.

AU - Rousseau, C. C.

AU - Schelp, R. H.

PY - 1994/3/15

Y1 - 1994/3/15

N2 - Let G be a graph on n vertices and let α and β be real numbers, 0 <α, β <1. Further, let G satisfy the condition that each ⌊αn⌋ subset of its vertex set spans at least βn2 edges. The following question is considered. For a fixed α what is the smallest value of β such that G contains a triangle?

AB - Let G be a graph on n vertices and let α and β be real numbers, 0 <α, β <1. Further, let G satisfy the condition that each ⌊αn⌋ subset of its vertex set spans at least βn2 edges. The following question is considered. For a fixed α what is the smallest value of β such that G contains a triangle?

UR - http://www.scopus.com/inward/record.url?scp=38149148150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149148150&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(92)00474-6

DO - 10.1016/0012-365X(92)00474-6

M3 - Article

VL - 127

SP - 153

EP - 161

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -