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Theorem on Hamiltonian graphs
In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that
Fleischner's_theorem
Path in a graph that visits each vertex exactly once
path through all edges in a graph Fleischner's theorem, on Hamiltonian squares of graphs Gray code Grinberg's theorem giving a necessary condition for
Hamiltonian_path
Austrian mathematician
of the theorem according to which the square of every two-connected graph has a Hamiltonian cycle. This result (now known as Fleischner's theorem) had been
Herbert_Fleischner
Graph of short distances in another graph
to determine whether the square is Hamiltonian. Nevertheless, by Fleischner's theorem, the square of a 2-vertex-connected graph is always Hamiltonian.
Graph_power
Hamiltonian. Chvátal's original conjecture that t = 2 would have proven Fleischner's theorem but was disproved by Bauer, Broersma & Veldman (2000). The existence
Graph_toughness
Graph containing cycles of all possible lengths
{\displaystyle k} . If G {\displaystyle G} is 2-vertex-connected, then by Fleischner's theorem its square G 2 {\displaystyle G^{2}} is Hamiltonian; this can be
Pancyclic_graph
Variant of the traveling salesman problem
weight being no more than twice the optimum. This result follows by Fleischner's theorem, that the square of a 2-vertex-connected graph always contains a
Bottleneck traveling salesman problem
Bottleneck_traveling_salesman_problem
Topics referred to by the same term
the pseudonymous author of a 1978 mathematics paper concerning Fleischner's theorem Paris Underground, a musical group whose members included Colm Farrelly
Paris_Underground
In graph theory, the Graham–Pollak theorem states that the edges of an n {\displaystyle n} -vertex complete graph cannot be partitioned into fewer than
Graham–Pollak_theorem
Non-crossing graph with vertices on outer face
Chvátal's watchman theorem", Journal of Combinatorial Theory, Series B, 24 (3): 374, doi:10.1016/0095-8956(78)90059-X. Fleischner, Herbert J.; Geller
Outerplanar_graph
American mathematician
of several mathematicians to conjecture the result now known as Fleischner's theorem on Hamiltonian cycles in squares of graphs. Plummer is a Foundation
Michael_D._Plummer
Cycles in a graph that cover each edge twice
matchings (that is, the graph has no 3-edge coloring, and by Vizing's theorem has chromatic index 4). It turns out that snarks form the only difficult
Cycle_double_cover
has 11 vertices but has maximum degree 5 and is not regular. By Brooks’ theorem, every k {\displaystyle k} -regular graph (except for odd cycles and cliques)
Chvátal_graph
Trail in a graph that visits each edge once
published posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an
Eulerian_path
Graph representing faces of another graph
two regions, the inside and outside of the cycle, by the Jordan curve theorem. However, in an n-cycle, these two regions are separated from each other
Dual_graph
1959) – mathematician who proved (with Robert I. Soare) the low basis theorem, with applications to recursion theory and reverse mathematics Steven E
List of Vanderbilt University people
List_of_Vanderbilt_University_people
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FLEISCHNERS THEOREM
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