Hamiltonian path

Barnette's conjecture, an open problem on Hamiltonicity of cubic bipartite polyhedral graphs

Eulerian path, a path through all edges in a graph

Fleischner's theorem, on Hamiltonian squares of graphs

Grinberg's theorem giving a necessary condition for planar graphs to have a Hamiltonian cycle

Hamiltonian path problem, the computational problem of finding Hamiltonian paths

Hypohamiltonian graph, a non-Hamiltonian graph in which every vertex-deleted subgraph is Hamiltonian

Knight's tour, a Hamiltonian cycle in the knight's graph

LCF notation for Hamiltonian cubic graphs.

Lovász conjecture that vertex-transitive graphs are Hamiltonian

Pancyclic graph, graphs with cycles of all lengths including a Hamiltonian cycle

Panconnectivity, a strengthening of both pancyclicity and Hamiltonian-connectedness

Shortness exponent, a numerical measure of how far from Hamiltonian the graphs in a family can be

Snake-in-the-box, the longest induced path in a hypercube

Steinhaus–Johnson–Trotter algorithm for finding a Hamiltonian path in a permutohedron

Subhamiltonian graph, a subgraph of a planar Hamiltonian graph

Tait's conjecture (now known false) that 3-regular polyhedral graphs are Hamiltonian

Harris graphs, a family of graphs that are tough, Eulerian, and non-Hamiltonian