Mixed-Integer Cuts from Cyclic Groups -- Optimizing over the First Chvàtal Closure -- Sequential Pairing of Mixed Integer Inequalities -- Approximate Min-max Relations for Odd Cycles in Planar Graphs -- Disjoint Cycles: Integrality Gap, Hardness, and Approximation -- A Combinatorial Algorithm to Find a Maximum Even Factor -- Improved Approximation Schemes for Linear Programming Relaxations of …