discrete mathematics - What is the difference between a Hamiltonian ...
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 …
Reduction from Hamiltonian cycle to Hamiltonian path
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, …
How many Hamiltonian cycles are there in a complete graph $K_n$ ($n ...
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.
Understanding the reduction from Hamiltonian cycle to the traveling ...
Dec 22, 2014 · The traveling salesman problem is NP-complete. Proof First, we have to prove that TSP belongs to NP. If we want to check a tour for credibility, we check that the tour contains each vertex …
Connected graph - 5 vertices eulerian not hamiltonian
Nov 6, 2014 · i need to give an example of a connected graph with at least 5 vertices that has as an Eulerian circuit, but no Hamiltonian cycle?
Hamiltonian of a particle in a magnetic field - Physics Forums
Feb 4, 2022 · Now the author in Chapter 3 introduces the Hamiltonian operator as "The eigenvalues of the Hamiltonian are the allowed energies of the quantum system, and the eigenstates of are the …
When does the exchange operator commute with the Hamiltonian
Mar 19, 2020 · Some participants assert that if the Hamiltonian treats two particles identically, then the exchange operator must commute with the Hamiltonian. Others argue that the key factor is the …
Proof of Hamiltonian Cycle in a Complete Bipartite Graph
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 …
real analysis - Level sets and orbits of a Hamiltonian system ...
Mar 16, 2025 · It is conjectured that for dimension at least $6$, a generic Hamiltonian admits orbits that are dense in most level sets. If this is not true, one may consider the set of points that are reachable …
Deriving the Hamiltonian of a system given the Lagrangian
Jan 4, 2024 · The Hamiltonian for the system derived from the Lagrangian is expressed as H = L - 6 (q_1)^2. The process involves calculating momenta using the equation p_i = δL/δ\dot {q_i} and …