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

Depends on #32197

Component: graph theory

Author: David Coudert

Branch/Commit: ebc2e90

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/32225