Topic: Hamiltonian Cycles and Sufficient Conditions

The Closure Theorem for Hamiltonian Graphs

The Chvatal–Erdos Hamiltonicity Condition

The Bondy–Chvátal Closure

Sufficient Conditions Are Not Characterizations

Sharpness of Dirac’s Minimum-Degree Bound

Sharpness of Ore’s Degree-Sum Bound

Ore’s Theorem: Statement and Examples

Necessary Conditions for Hamiltonicity

Hamiltonian Paths and Cycles

Hamiltonian Paths in Complete Bipartite Graphs