1 Introduction

2 Framework for Best Monotone Degree Conditions

3 Best Monotone Conditions for Graph Properties

3.1 Edge-Connectivity
3.2 Binding Number
3.3 Toughness
3.4 Factors
3.5 Paths and Cycles
3.6 Independence Number, Clique Number, Chromatic Number, and Vertex Arboricity

4 Best Monotone Degree Conditions for Implications

5 Improving Structural Results in a Best Monotone Sense