Have Arahants have eliminated all Sankhara? I read on the internet: 


  Arahants have eliminated all Sankhara. So there is no need for
  accumulation of memory.


Have Arahants really eliminated all Sankhara?

Please answer with Pali sutta references.
SN 22.85 says Arahants have "sankhara": 


  “If, friend Yamaka, they were to ask you: ‘Friend Yamaka, when a
  bhikkhu is an arahant, one whose taints are destroyed, what happens to
  him with the breakup of the body, after death?’—being asked thus, what
  would you answer?”
  
  “If they were to ask me this, friend, I would answer thus: ‘Friends,
  form is impermanent; what is impermanent is suffering; what is
  suffering has ceased and passed away. Feeling … Perception …
  Volitional formations … Consciousness is impermanent; what is
  impermanent is suffering; what is suffering has ceased and passed
  away.’ Being asked thus, friend, I would answer in such a way.”
  
  “Good, good, friend Yamaka!


MN 43 says a living individual has ayu-sankhara (vitality/life force): 


  But because the life forces and the phenomena that are felt are
  different things, a mendicant who has attained the cessation of
  perception and feeling can emerge from it.
  
  Yasmā ca kho, āvuso, aññe āyusaṅkhārā aññe vedaniyā dhammā, tasmā
  saññāvedayitanirodhaṃ samāpannassa bhikkhuno vuṭṭhānaṃ paññāyatī”ti.
  
  When a mendicant has attained the cessation of perception and feeling,
  their physical, verbal, and mental processes have ceased and stilled.
  But their vitality is not spent; their warmth is not dissipated; and
  their faculties are very clear.
  
  Yo cāyaṃ bhikkhu saññāvedayitanirodhaṃ samāpanno tassapi kāyasaṅkhārā
  niruddhā paṭippassaddhā, vacīsaṅkhārā niruddhā paṭippassaddhā,
  cittasaṅkhārā niruddhā paṭippassaddhā, āyu na parikkhīṇo, usmā
  avūpasantā, indriyāni vippasannāni.


MN 26 describes Nibbana as the "calming (samatho) of all sankhara" rather than "destruction of all sankhara": 


  It’s also hard for them to see this thing; that is, the stilling of
  all activities, the letting go of all attachments, the ending of
  craving, fading away, cessation, extinguishment.
  
  Idampi kho ṭhānaṃ duddasaṃ yadidaṃ—sabbasaṅkhārasamatho
  sabbūpadhipaṭinissaggo taṇhākkhayo virāgo nirodho nibbānaṃ.