# All Questions

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### The covering radius of $C=\{0000,1111\}$

Lets say I have the code $C=\{0000,1111\}$. Why is the covering radius $\rho=2$? How is the covering radius worked out?
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### Punctured plane is not simply connected

Adapt the following definition of "simply connected space" (taken from Wikipedia): A space $X$ is simply connected if it's path connected and for any continuous map $f:S^1\rightarrow X$ can be ...
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### Prove that, if both solutions of ${ x }^{ 2 }+ax+b=0$ are even integers, then a and b are both even integers.

Prove that, if both solutions of$${ x }^{ 2 }+ax+b=0$$are even integers, then a and b are both even integers. I don't even know where to start on this problem.
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### Prove that all linegraphs L(G) are claw free

For any graph G, prove that the line graph L(G) is claw-free. I have a fairly good intuition for this one but it's hard to put into words. I really need help with this one! I feel that I should use ...
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### Randomized Quick Sort and Partition Probability?

We know about Quick Sort and Randomized Version and Partition. I ran into a Fact when I read my notes. Let $0 < a < 0.5$ be some constant. We have an $n$-element array as input. Randomized ...

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