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Question: We consider a puzzle posed by Petkovi´c in [Pe09] (based on a problem in [AvCh80]). Suppose that King Arthur has gathered his 2n knights of the Round Table for an important council. Every two knights are either friends or enemies, and each knight has no more than n - 1 enemies among the other 2n - 1 knights. The puzzle asks whether King Arthur can seat his knights around the Round Table so that each knight has two friends for his neighbors
a) Show that the puzzle can be reduced to determining whether there is a Hamilton circuit in the graph in which each knight is represented by a vertex and two knights are connected in the graph if they are friends.
b) Answer the question posed in the puzzle.
What situations would make rectangular, cylindrical or spherical integration best? Is integration over other coordinate systems possible or ever ideal?
Write a 1-2 page essay analyzing the 2011 decision of the WTO regarding the Airbus /Boeing dispute or any other dispute that has been presented for determination to the WTO. Express your own opinion concerning the determination. (NO PLAGIARISM) If..
A salesman drives from Ajax to Barrington, a distance of 133 mi, at a steady speed. He then increases his speed by 15 mi/h to drive the 185 mi from Barrington to Collins. If the second leg of his trip took 15 min more time than the first leg, how ..
Find a recurrence relation for the number of ternary strings of length n that contain two consecutive 0s.
ow pitch softball diamond is actually a square 61 ft on a side. How far is it from home to second base?
Sketch the graphs of the following functions by hand, using transformations. Show your work (show how the transformations map from the base function to the transformed function) for the graph in addition to listing the information.
Solve The heat equation du/dt = d^2u / dx^2 (note: partial derivatives), u(x, 0) = sin^2(x), u(0, t) = 0, u(Pi, t) = 0, 0
A building is 172 feet tall. For a class project, Kari is to make a scale model of the building to place in the front hall display case. The display case is 22 inches tall. Which scale will allow her to make the tallest model that will fit in the ..
Provide two examples of radical expressions, that include variables. At least one of the examples must have more than one term.
jennifer has an exercise regimen at the local gym that includes using a treadmill stair machine and cycle. according to
A square support unit in a television is made with a side measuring 10 centimeters. A new model being designed for the upcoming year will have a larger square with a side measuring 10.3 centimeters
Sand is leaking from the back of a dump truck and forming a conical pile on the ground. The sand is leaking at the rate of 0.2 m3 per hour. If the base radius of the pile is always 0.6 times the height, how fast is the base radius changing when the ..
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