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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
Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept form.
What are the four categories of financial ratios? Choose one category (excluding liquidity ratios) and list and describe the various ratios in that category. What do the calculated numbers mean for these ratios?
For a statistics class project, students examined the relationship between x1 = 8th grade IQ, x2 = 8th grade Abstract Reasoning and y = 9th grade math scores for 20 students.
Is the approximate change larger or smaller than the actual change?
Computer analysis showed that the surface of a certain drumlin can be approximated by y= 10(1-0.0001x^2) revolved 180 about the x-axis from x= -100 to 100.
The profit generated by each individual resident expert for each design job
Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Define Tree Diagram and Dice Tossing
find the negation of each of the following statementsa john is tall and likes to bike.b mike will laugh or cry
The function P(t) = 145e-0.092t models a runner's pulse, P(t), in beats per minute, t minutes after a race, where 0 ≤ t ≤15. Graph the function using a graphing utility. TRACE along the graph and determine after how many minutes the runner's puls..
Compute the population mean, m. List all possible samples with size n = 2. There should be 6C2 = 15 samples. Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities
A company determines that its marginal revenue per day is given by Upper R prime left parenthesis t right parenthesisR(t),where Upper R left parenthesis t right parenthesisR(t)is the total accumulatedrevenue, indollars, on the tth day. Thecompany's m..
Find all nonnegative integer values for x and y that satisfy the equation 740x + 1295y = 18,500, and determine the possible computer purchases for the department.
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