Part of #32191 (Meta-ticket: Audit/fix all uses of MixedIntegerLinearProgram? in sage.combinat, sage.graphs).

Depends on #32197

CC: @mkoeppe @tscrim @dimpase

Component: graph theory

Author: David Coudert

Branch/Commit: 9223c66

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/32223