theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or...

The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G...

optimal control for a dynamical system Hamiltonian path, a path in a graph that visits each vertex exactly once Hamiltonian matrix, a matrix with certain special...

includes every vertex of the graph without repeats is known as a Hamiltonian path. Two paths are vertex-independent (alternatively, internally disjoint or...

critical path in scheduling problems. The NP-hardness of the unweighted longest path problem can be shown using a reduction from the Hamiltonian path problem:...

The Petersen graph has a Hamiltonian path but no Hamiltonian cycle. It is the smallest bridgeless cubic graph with no Hamiltonian cycle. It is hypohamiltonian...

directed Hamiltonian path in the DAG. If a Hamiltonian path exists, the topological sort order is unique; no other order respects the edges of the path. Conversely...

odd-degree vertices Hamiltonian path – a path that visits each vertex exactly once. Route inspection problem, search for the shortest path that visits all...

toroidal graph has a Hamiltonian cycle, and (with W. Zang) that every 4-vertex-connected toroidal graph has a Hamiltonian path. Kawarabayashi, Ken-ichi;...

general Hamiltonian path problem in graph theory. The problem of finding a closed knight's tour is similarly an instance of the Hamiltonian cycle problem...

find a Hamiltonian cycle with the least weight. This is more general than the Hamiltonian path problem, which only asks if a Hamiltonian path (or cycle)...

a Hamiltonian path? More unsolved problems in mathematics In graph theory, the Lovász conjecture (1969) is a classical problem on Hamiltonian paths in...

path if and only if there is a Hamiltonian path in G. The Hamiltonian path problem is NP-complete, and hence the minimum path cover problem is NP-hard. However...

Hamilton's work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory. He also invented the icosian game as a...

finite number n {\displaystyle n} of vertices contains a Hamiltonian path, i.e., directed path on all n {\displaystyle n} vertices (Rédei 1934). This is...

mechanics Hamiltonian optics Hamiltonian principle, see Hamilton's principle Hamiltonian system Hamiltonian vector field In mathematics: Hamiltonian path, in...

proof-of-concept use of DNA as a form of computation which solved the seven-point Hamiltonian path problem. Since the initial Adleman experiments, advances have occurred...

would create at least one new Hamiltonian cycle, and the edges other than xy in such a cycle must form a Hamiltonian path v1v2...vn in H with x = v1 and...

an Archimedean solid. It is one of six Catalan solids to not have a Hamiltonian path among its vertices. It is topologically identical to the nonconvex...

Shortest Path First Flooding algorithm Route inspection problem Hamiltonian path Hamiltonian path problem Knight's tour Traveling salesman problem Nearest neighbour...

never less than the chromatic number. Hamiltonian A Hamiltonian path or Hamiltonian cycle is a simple spanning path or simple spanning cycle: it covers...

+ 12 = 12312 = 312. Any Hamiltonian path through the created graph is a superpermutation, and the problem of finding the path with the smallest weight...

to make them Hamiltonian. Wu, Q. S.; Lu, Chin Lung; Lee, Richard C. T. (2000), "An approximate algorithm for the weighted Hamiltonian path completion problem...

W. T. Tutte states that every 4-vertex-connected planar graph has a Hamiltonian cycle. It strengthens an earlier theorem of Hassler Whitney according...

program E. coli to solve complicated mathematics problems, such as the Hamiltonian path problem. A computer to control protein production of E. coli within...

enters the path integrals (for interactions of a certain type, these are coordinate space or Feynman path integrals), than the Hamiltonian. Possible downsides...

hypercube Qn with n > 1 has a Hamiltonian cycle, a cycle that visits each vertex exactly once. Additionally, a Hamiltonian path exists between two vertices...

Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed by...

physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics...

Hamiltonian mechanics Hamilton–Jacobi equation, a set of physical equations in Hamiltonian mechanics Hamiltonian (quantum mechanics) Hamiltonian path...