Proof of `Day-Independent Due Dates and Processing Times` (1st statement)
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Colour the clients greedily in the order in which their jobs start: when a job is coloured, the jobs already coloured that it meets are all running at the instant it starts, so they and it form a clique, and a colour below the clique number is free.