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 the web, …

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 closed trail in …

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.

Dec 19, 2019 · Explore related questions graph-theory hamiltonian-path hamiltonicity See similar questions with these tags.

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 starting point.

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 formulated L …

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 hamiltonian ): – David …

Hamiltonian path is a path that contains all of the vertices of the graph. I know that if $deg (u)+deg (v) \ge n$ for every two non adjacent vertices $u$ and $v$ then the graph has Hamiltonian cycle and …

This is trivially Hamiltonian in that there is a zero length path that visits the vertex. [1] Part 3: If m = 1 xor n = 1, the graph is not Hamiltonian All Hamiltonian graphs are biconnected. [2] If exactly one of the …

Your proof looks good. I would justify the existence of a repeated vertex using the pigeonhole principle. You also say here: "This leads to a contradiction since a cycle cannot have repeating vertices." I …