mididhs

hamiltonian cycle

a cycle that includes every vertex in the graph. no repeated edges or vertices, except for the vertex at the very beginning which is the same as the very last one.

hamiltonian path

a path that includes every vertex in the graph, no repeated edges or vertices, every vertex appears exactly once

how to turn a hamiltonian cycle into a hamiltonian path

delete the last vertex

euler circuit

a circuit that contains every edge and every vertex, with every edge being accounted for with no repetition of edges. vertex can be passed through more than once

if any vertex has an odd degree, it cannot have a euler circuit

euler trail

an open trail that incldues every edge and every vertex, with every edge being included and accounted for only once

exactly two edges have an odd degree. said two are eiether end or start