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mikespivey.wordpress.com | ||
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dominiczypen.wordpress.com
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| | | | | Suppose you want to have a graph $latex G = (V,E)$ with chromatic number $latex \chi(G)$ equaling some value $latex k$, such that $latex G$ is minimal with this property. So you end up with a $latex k$-(vertex-)critical graph. It is easy to construct critical graphs by starting with some easy-to-verify example like $latex C_5$... | |
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pfzhang.wordpress.com
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| | | | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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boonaree.wordpress.com
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