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Rainbow Coloring
In graph theory, a path in an edge-colored graph is said to be rainbow if no color repeats on it. A graph is said to be rainbow-connected (or rainbow colored) if there is a rainbow path between each pair of its vertices. If there is a rainbow shortest path between each pair of vertices, the graph is said to be strongly rainbow-connected (or strongly rainbow colored). Definitions and bounds The rainbow connection number of a graph G is the minimum number of colors needed to rainbow-connect G, and is denoted by \text(G). Similarly, the strong rainbow connection number of a graph G is the minimum number of colors needed to strongly rainbow-connect G, and is denoted by \text(G). Clearly, each strong rainbow coloring is also a rainbow coloring, while the converse is not true in general. It is easy to observe that to rainbow-connect any connected graph G, we need at least \text(G) colors, where \text(G) is the diameter of G (i.e. the length of the longest shortest path). On the ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wheel Rainbow Coloring
A wheel is a circular component that is intended to rotate on an axle bearing. The wheel is one of the key components of the wheel and axle which is one of the six simple machines. Wheels, in conjunction with axles, allow heavy objects to be moved easily facilitating movement or transportation while supporting a load, or performing labor in machines. Wheels are also used for other purposes, such as a ship's wheel, steering wheel, potter's wheel, and flywheel. Common examples are found in transport applications. A wheel reduces friction by facilitating motion by rolling together with the use of axles. In order for wheels to rotate, a moment needs to be applied to the wheel about its axis, either by way of gravity or by the application of another external force or torque. Using the wheel, Sumerians invented a device that spins clay as a potter shapes it into the desired object. Terminology The English word ''wheel'' comes from the Old English word , from Proto-Germanic , from P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
