After much searching I found it!!!

https://forums.totalwar.org/vb/newre...te=1&p=1777549

Quote Originally Posted by Younger, Sexier and Obviously More Intelligent Me
Five Honour 0 units fought two Honour 2 Units on custom.

All the Honour 0 men who lived and had killed one person where rank 2.

All the Honour 0 men who lived and had killed two people where rank 3.

Many of the Honour 2 men who killed one or two opponents stayed at rank 2. I speculate that the ones who did increase in rank killed a freshly minted rank 2 opponent (rank 0 killed rank 2 went to rank 2, then killed by one of the original rank 2 comrades).

I believe it is a binary formula where going up one rank takes;

2^(current rank) honour kills [hk].

Routing opponents = 0 honour
Honour Kill rating of an opponent = 2^(honour rank)

So a rank 0 opponent is worth one hk.
And a rank 2 opponent is worth 4 hks.

To get to rank 1 from rank 0 takes one hk.
To get to rank 2 from rank 1 takes two hks.
To get to rank 3 from rank 2 takes four hks.

So if you kill someone of higher honour who is not routing you will go to their rank.

If you kill someone of equal rank you will go up one rank.

Daimyo are honour rank 5. So kill one and you will progress to at least rank 5.

Generals are sometimes rank 3. So if they die they will trigger the legendary swordsmen event (assuming their killer survives)