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Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
The computation of the Hausdorff dimension of the graph of the classical Weierstrass function was an open problem until 2018, while it was generally believed that = + <. [6] [7] That D is strictly less than 2 follows from the conditions on and from above. Only after more than 30 years was this proved rigorously.
The secular variation of a time series is its long-term, non-periodic variation (see Decomposition of time series).Whether a variation is perceived as secular or not depends on the available timescale: a variation that is secular over a timescale of centuries may be a segment of what is, over a timescale of millions of years, a periodic variation.
The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
Finding the shortest solution sequence in the pebble motion on graphs problem (with labeled pebbles) is known to be NP-hard [6] and APX-hard. [3] The unlabeled problem can be solved in polynomial time when using the cost metric mentioned above (minimizing the total number of moves to adjacent vertices), but is NP-hard for other natural cost ...
A radial hyperbolic trajectory is a non-periodic trajectory on a straight line where the relative speed of the two objects always exceeds the escape velocity. There are two cases: the bodies move away from each other or towards each other. This is a hyperbolic orbit with semi-minor axis = 0 and eccentricity = 1.
An example of a spider web projection of a trajectory on the graph of the logistic map, and the locations of the fixed points and on the graph. Graphs of maps, especially those of one variable such as the logistic map, are key to understanding the behavior of the map.