Mantel's theorem: the triangle-free case

\(\lfloor n^2/4 \rfloor\) edges, attained by the balanced complete bipartite graph. The floor matters at odd \(n\).

Usage

morie_mantel_number(n)

Arguments

n

Vertices.

Value

As morie_turan_number(), with floor_n2_over_4.

References

Mantel W (1907). Problem 28. Wiskundige Opgaven, 10, 60-61.

Examples

morie_mantel_number(n = 5L)
#> $count
#> [1] 6
#> 
#> $rounded_formula
#> [1] 6.25
#> 
#> $formula_is_exact
#> [1] FALSE
#> 
#> $part_sizes
#> [1] 3 2
#> 
#> $construction_edges
#> [1] 6
#> 
#> $attained
#> [1] TRUE
#> 
#> $forbidden_clique
#> [1] 3
#> 
#> $n
#> [1] 5
#> 
#> $r
#> [1] 2
#> 
#> $method
#> [1] "Mantel's theorem (Mantel 1907)"
#> 
#> $floor_n2_over_4
#> [1] 6
#>