A Hamiltonian circuit (or cycle) visits every vertex exactly once before returning to its starting point. An Eulerian circuit visits every edge exactly once in the graph before returning to the …

Aug 18, 2020 · Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once Hamiltonian cycle is a Hamiltonian path that is a cycle, and a cycle is …

Oct 18, 2010 · I'm looking for an explanation on how reducing the Hamiltonian cycle problem to the Hamiltonian path's one (to proof that also the latter is NP-complete). I couldn't find any on …

Nov 24, 2019 · Hamiltonian cycle implies biconnected, which in turn implies that every node has degree at least two. Hamiltonian path implies connected and at most two nodes of degree one.

Apr 9, 2020 · – David Hernández Uriostegui Apr 9, 2020 at 19:55 Hey N.S but for example the 6-regular graph with 10 vertexs is hamiltonian, but its complement is connected and not …

There are $\frac {n-1} {2}$ such consecutive pairs in the upper half of the circumference with $\frac {n-1} {2}$ edges connecting them each leading to unique edge disjoint Hamiltonian circuits.

Nov 16, 2017 · Hello, I am trying to "integrate into my understanding" the difference between Hamiltonian and Lagrangian mechanics. In a nutshell: If Lagrange did all the work and …

In case you need more clarification from user121270's comment: If the degree condition holds, the graph is Hamiltonian. But it's not necessarily the case that every Hamiltonian graph also …

Feb 21, 2022 · If $G$ is a graph of order $n \ge 3$ such that $\deg v \ge n/2$ for each vertex of $G$, then $G$ is Hamiltonian.

As mentioned in the other answer by Gerry Myerson, there is no simple neccessary and sufficient condition, since the problem of determining if a general graph has a Hamiltonian Path is NP …