# Maximal triangle‐free graphs with restrictions on the degrees

Z. Füredi, Ákos Seress

Research output: Contribution to journalArticle

9 Citations (Scopus)

### Abstract

We investigate the problem that at least how many edges must a maximal triangle‐free graph on n vertices have if the maximal valency is ≤D. Denote this minimum value by F(n, D). For large enough n, we determine the exact value of F(n, D) if D ≥ (n − 2)/2 and we prove that lim F(n, cn)/n = K(c) exists for all 0 < c with the possible exception of a sequence ck → 0. The determination of K(c) is a finite problem on all intervals [γ, ∞). For D = cnϵ, 1/2 < ϵ < 1, we give upper and lower bounds for F(n, D) differing only in a constant factor. (Clearly, D < (n ‐ 1)1/2 is impossible in a maximal triangle‐free graph.)

Original language English 11-24 14 Journal of Graph Theory 18 1 https://doi.org/10.1002/jgt.3190180103 Published - 1994

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### ASJC Scopus subject areas

• Geometry and Topology

### Cite this

In: Journal of Graph Theory, Vol. 18, No. 1, 1994, p. 11-24.

Research output: Contribution to journalArticle

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