An improvement to Chvátal and Thomassen’s upper bound for oriented diameter

Improved bounds for the oriented radius of mixed multigraphs

“…Kwok, Liu, and West [13] proved that ≤ ≤ g 9 ¯(3) 11. Together with Vaka, we showed that ≤ g ¯(4) 21 [2]. The major focus in [2] .…”

“…Together with Vaka, we showed that ≤ g ¯(4) 21 [2]. The major focus in [2] . Extensions of this line of attack to mixed graphs to obtain better bounds for g d ( ) (bypassing f r ( )) are still open.…”

“…Kwok, Liu, and West [13] proved that $$9\le \bar{g}(3)\le 11$$. Together with Vaka, we showed that $$\bar{g}(4)\le 21$$ [2]. The major focus in [2] was to show that $$\bar{g}(d)\le 1.373{d}^{2}+6.971d-1$$.…”

“…Together with Vaka, we showed that $$\bar{g}(4)\le 21$$ [2]. The major focus in [2] was to show that $$\bar{g}(d)\le 1.373{d}^{2}+6.971d-1$$. Extensions of this line of attack to mixed graphs to obtain better bounds for $$g(d)$$ (bypassing $$f(r)$$) are still open.…”

“…in Equation (2). Notice that, when η is even, this term sums up odd numbers from 1 to η − 3 and when η is odd, the term sums up even numbers from 0 to η − 3.…”