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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

/ 2 {\displaystyle (n-1)/2} Hamiltonian paths that zigzag across the polygon, with each path rotated from each other path by a multiple of π / ( n − 1...

contain a Hamiltonian cycle. It states that, if G {\displaystyle G} is a 2-vertex-connected graph, then the square of G {\displaystyle G} is Hamiltonian. It...

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...

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...

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...

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

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...

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

Panconnected graphs are also a generalization of Hamiltonian-connected graphs (graphs that have a Hamiltonian path connecting every pair of vertices). Several...

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...

line graph of an arbitrary tree so that it contains a Hamiltonian path (the size of its Hamiltonian completion) equals the minimum number of edge-disjoint...

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