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- Horton_graph abstract "In the mathematical field of graph theory, the Horton graph or Horton 96-graph is a 3-regular graph with 96 vertices and 144 edges discovered by Joseph Horton. Published by Bondy and Murty in 1976, it provides a counterexample to the Tutte conjecture that every cubic 3-connected bipartite graph is Hamiltonian.After the Horton graph, a number of smaller counterexamples to the Tutte conjecture were found. Among them are a 92 vertices graph by Horton published in 1982, a 78 vertices graph by Owens published in 1983, and the two Ellingham-Horton graphs (54 and 78 vertices).The first Ellingham-Horton graph was published by Ellingham in 1981 and was of order 78. At that time, it was the smallest know counterexample to the Tutte conjecture. The second one was published by Ellingham and Horton in 1983 and was of order 54. No smaller non-hamiltonian cubic 3-connected bipartite graph is currently known.As a non-hamiltonian cubic graph with many long cycles, the Horton graph provides good benchmark for programs that search for Hamiltonian cycles.The Horton graph has chromatic number 2, chromatic index 3, radius 10, diameter 10 and girth 6. It is also a 3-edge-connected graph.".
- Horton_graph thumbnail Horton_graph.svg?width=300.
- Horton_graph wikiPageID "24116567".
- Horton_graph wikiPageRevisionID "545707537".
- Horton_graph automorphisms "96".
- Horton_graph chromaticIndex "3".
- Horton_graph chromaticNumber "2".
- Horton_graph diameter "10".
- Horton_graph edges "144".
- Horton_graph girth "6".
- Horton_graph hasPhotoCollection Horton_graph.
- Horton_graph imageCaption "The Horton graph".
- Horton_graph name "Horton graph".
- Horton_graph namesake "Joseph Horton".
- Horton_graph properties Bipartite_graph.
- Horton_graph properties Cubic_graph.
- Horton_graph radius "10".
- Horton_graph vertices "96".
- Horton_graph subject Category:Individual_graphs.
- Horton_graph subject Category:Regular_graphs.
- Horton_graph type Abstraction100002137.
- Horton_graph type Communication100033020.
- Horton_graph type Graph107000195.
- Horton_graph type IndividualGraphs.
- Horton_graph type RegularGraphs.
- Horton_graph type VisualCommunication106873252.
- Horton_graph comment "In the mathematical field of graph theory, the Horton graph or Horton 96-graph is a 3-regular graph with 96 vertices and 144 edges discovered by Joseph Horton. Published by Bondy and Murty in 1976, it provides a counterexample to the Tutte conjecture that every cubic 3-connected bipartite graph is Hamiltonian.After the Horton graph, a number of smaller counterexamples to the Tutte conjecture were found.".
- Horton_graph label "Graphe de Horton".
- Horton_graph label "Horton graph".
- Horton_graph sameAs Graphe_de_Horton.
- Horton_graph sameAs m.07kcfl2.
- Horton_graph sameAs Q3115508.
- Horton_graph sameAs Q3115508.
- Horton_graph sameAs Horton_graph.
- Horton_graph wasDerivedFrom Horton_graph?oldid=545707537.
- Horton_graph depiction Horton_graph.svg.
- Horton_graph isPrimaryTopicOf Horton_graph.