Proof of `Per-Client Fairness Parameters at Treewidth Four` (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
The vertex-selection gadget of a colour compels one vertex client of that colour, the validation day pushes its incidence clients onto their edge days, and the two interaction clients, needing half the edge days each, leave one of the two incidence clients of every edge unserved. The dummy client blocks exactly the clients parked on a day, so each day reduces to its gadget.