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A. Show that the tree-order associated with a rooted tree T is indeed a partial order on V(T), and verify the claims made about this partial order in the text.B. Do the partition classes of a regular bipartite graph always have the same size?
C. Show that a graph is bipartite if and only if every induced cycle has even length.
D. Find a function f : N → N such that, for all k ∈ N, every graph of average degree at least f(k) has a bipartite subgraph of minimum degree at least k.
A person must select 3 numbers from 18 numbers for a single ticket in a lottery game. Only one number has to match in order to win a prize. Find the probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.)..
a ladder 20 feet long leans against the side of a house. find the height from the top of the ladder to the ground if
question sam and martha are local names for two lighthouses. sam blinks every 12 seconds martha every 8 seconds. they
Show that == (where == is the equivalence relation defined below) is an equivalence on A, and find a (well-defined) bijection %: A== -> B, where
Probability - birthday, What is the probability that at least 2 of the 435 members of the House of Representatives have the same birthday
a car travels along a straight road heading east for 1 h then traveling for 30 min on another road that leads
How many tennis rackets of each type should CSD manufacture over the next two weeks to maximize the total profit contribution? Assume that because of the unique nature of their products, CSD can sell as many rackets as they can produce.
For which values of k are the following vectors u and v orthogonal? Let u,v be orthogonal unit vectors. Prove that d(u,v) = 2^(1/2)
Megs pension plan is an annuity with a guaranteed return
Compute the derivative of the given function and find the equation of the line that is tangent to its graph for the specified value of x0.
evaluate the maximum revenue using cost and revenue function.the manager of a cd store has found that if the price of a
How do you plot the volume of water in the sink as a volume of water?
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