### Abstract

A triangle‐free graph is maximal if adding any edge will create a triangle. The minimal number of edges of a maximal triangle‐free graph on n vertices having maximal degree at most D is denoted by F(n, D). We determine the value of lim_{n‐∞} F(n, cn)/n for 2/5 < c < 1/2. This investigation continues work done by Z. Füredi and Á. Seress. Our result is contrary to a conjecture of theirs.

Original language | English |
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Pages (from-to) | 585-594 |

Number of pages | 10 |

Journal | Journal of Graph Theory |

Volume | 18 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1994 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*18*(6), 585-594. https://doi.org/10.1002/jgt.3190180606

**On maximal triangle‐free graphs.** / Erdős, P.; Holzman, Ron.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 18, no. 6, pp. 585-594. https://doi.org/10.1002/jgt.3190180606

}

TY - JOUR

T1 - On maximal triangle‐free graphs

AU - Erdős, P.

AU - Holzman, Ron

PY - 1994

Y1 - 1994

N2 - A triangle‐free graph is maximal if adding any edge will create a triangle. The minimal number of edges of a maximal triangle‐free graph on n vertices having maximal degree at most D is denoted by F(n, D). We determine the value of limn‐∞ F(n, cn)/n for 2/5 < c < 1/2. This investigation continues work done by Z. Füredi and Á. Seress. Our result is contrary to a conjecture of theirs.

AB - A triangle‐free graph is maximal if adding any edge will create a triangle. The minimal number of edges of a maximal triangle‐free graph on n vertices having maximal degree at most D is denoted by F(n, D). We determine the value of limn‐∞ F(n, cn)/n for 2/5 < c < 1/2. This investigation continues work done by Z. Füredi and Á. Seress. Our result is contrary to a conjecture of theirs.

UR - http://www.scopus.com/inward/record.url?scp=84987472611&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987472611&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190180606

DO - 10.1002/jgt.3190180606

M3 - Article

VL - 18

SP - 585

EP - 594

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 6

ER -