• Thumbnail for Hamiltonian path
    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...
    19 KB (2,043 words) - 13:05, 14 May 2025
  • 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...
    21 KB (2,518 words) - 19:02, 20 August 2024
  • Thumbnail for Path (graph theory)
    includes every vertex of the graph without repeats is known as a Hamiltonian path. Two paths are vertex-independent (alternatively, internally disjoint or...
    10 KB (1,175 words) - 02:08, 11 February 2025
  • 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...
    1 KB (207 words) - 13:25, 12 October 2024
  • 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:...
    22 KB (2,662 words) - 06:47, 12 May 2025
  • 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...
    23 KB (3,170 words) - 01:52, 12 February 2025
  • Thumbnail for Petersen graph
    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...
    24 KB (2,993 words) - 04:57, 12 April 2025
  • Thumbnail for Eulerian path
    odd-degree vertices Hamiltonian path – a path that visits each vertex exactly once. Route inspection problem, search for the shortest path that visits all...
    29 KB (3,456 words) - 12:30, 30 May 2025
  • Thumbnail for Path cover
    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...
    4 KB (446 words) - 20:10, 17 January 2025
  • Thumbnail for Knight's tour
    Knight's tour (category Hamiltonian paths and cycles)
    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...
    22 KB (2,318 words) - 14:05, 21 May 2025
  • Thumbnail for Travelling salesman problem
    Travelling salesman problem (category Hamiltonian paths and cycles)
    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)...
    87 KB (11,633 words) - 21:17, 27 May 2025
  • Thumbnail for Hamiltonian decomposition
    / 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...
    15 KB (1,760 words) - 21:27, 30 May 2025
  • 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...
    4 KB (449 words) - 02:24, 20 January 2025
  • 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...
    11 KB (1,585 words) - 19:06, 10 January 2025
  • Thumbnail for Deltoidal hexecontahedron
    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...
    7 KB (636 words) - 13:51, 18 April 2025
  • Thumbnail for Fleischner's theorem
    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...
    14 KB (1,515 words) - 10:39, 12 January 2024
  • Lovász conjecture (category Hamiltonian paths and cycles)
    a Hamiltonian path? More unsolved problems in mathematics In graph theory, the Lovász conjecture (1969) is a classical problem on Hamiltonian paths in...
    8 KB (1,003 words) - 00:04, 12 March 2025
  • Thumbnail for Tournament (graph theory)
    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...
    19 KB (2,662 words) - 03:13, 20 January 2025
  • Tait's conjecture (category Hamiltonian paths and cycles)
    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...
    5 KB (638 words) - 22:42, 27 February 2025
  • Thumbnail for DNA computing
    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...
    43 KB (4,922 words) - 19:27, 26 April 2025
  • Shortest Path First Flooding algorithm Route inspection problem Hamiltonian path Hamiltonian path problem Knight's tour Traveling salesman problem Nearest neighbour...
    7 KB (663 words) - 02:52, 24 September 2024
  • In mathematics, the Hamiltonian cycle polynomial of an n×n-matrix is a polynomial in its entries, defined as ham ⁡ ( A ) = ∑ σ ∈ H n ∏ i = 1 n a i , σ...
    12 KB (2,239 words) - 13:15, 12 August 2024
  • Thumbnail for Superpermutation
    + 12 = 12312 = 312. Any Hamiltonian path through the created graph is a superpermutation, and the problem of finding the path with the smallest weight...
    11 KB (1,202 words) - 10:55, 6 February 2025
  • Thumbnail for Panconnectivity
    Panconnected graphs are also a generalization of Hamiltonian-connected graphs (graphs that have a Hamiltonian path connecting every pair of vertices). Several...
    3 KB (286 words) - 04:25, 2 February 2025
  • never less than the chromatic number. Hamiltonian A Hamiltonian path or Hamiltonian cycle is a simple spanning path or simple spanning cycle: it covers...
    109 KB (16,011 words) - 18:32, 30 April 2025
  • mechanics Hamiltonian optics Hamiltonian principle, see Hamilton's principle Hamiltonian system Hamiltonian vector field In mathematics: Hamiltonian path, in...
    3 KB (296 words) - 18:15, 13 October 2022
  • Thumbnail for Caterpillar tree
    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...
    10 KB (1,205 words) - 03:27, 5 October 2024
  • Thumbnail for Ore's theorem
    Ore's theorem (category Hamiltonian paths and cycles)
    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...
    9 KB (1,040 words) - 19:28, 26 December 2024
  • Thumbnail for Seven Bridges of Königsberg
    featured in different charity events. Eulerian path Five room puzzle Glossary of graph theory Hamiltonian path Icosian game Travelling salesman problem Three...
    15 KB (1,789 words) - 14:05, 4 May 2025
  • Thumbnail for Path integral formulation
    enters the path integrals (for interactions of a certain type, these are coordinate space or Feynman path integrals), than the Hamiltonian. Possible downsides...
    86 KB (14,277 words) - 08:57, 19 May 2025