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

Depends on #32197

CC: @jhpalmieri @dimpase @dcoudert @tscrim

Component: algebraic topology

Author: Matthias Koeppe

Branch/Commit: 63f7a15

Reviewer: John Palmieri, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32219