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Contents Index Embed Dark Mode Prev Up Next \(\usepackage{cancel}
\def\d{\displaystyle}
\def\N{\mathbb N}
\def\B{\mathbf B}
\def\Z{\mathbb Z}
\def\Q{\mathbb Q}
\def\R{\mathbb R}
\def\C{\mathbb C}
\def\U{\mathcal U}
\def\x{\mathbf{x}}
\def\y{\mathbf{y}}
\def\X{\mathcal{X}}
\def\Y{\mathcal{Y}}
\def\pow{\mathcal P}
\def\inv{^{-1}}
\def\st{:}
\def\iff{\leftrightarrow}
\def\Iff{\Leftrightarrow}
\def\imp{\rightarrow}
\def\Imp{\Rightarrow}
\def\isom{\cong}
\def\bar{\overline}
\def\card#1{\left| #1 \right|}
\def\twoline#1#2{\begin{pmatrix}#1 \\ #2 \end{pmatrix}}
\def\mchoose#1#2{
\left.\mathchoice
{\left(\kern-0.48em\binom{#1}{#2}\kern-0.48em\right)}
{\big(\kern-0.30em\binom{\smash{#1}}{\smash{#2}}\kern-0.30em\big)}
{\left(\kern-0.30em\binom{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
{\left(\kern-0.30em\binom{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
\right.}
\def\o{\circ}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Worksheet Preview Activity
For each graph below:
Find a proper vertex coloring using some number of colors. That is, color vertices using any number of colors but in such a way that no pair of adjacent vertices have the same color.
Find the
fewest number of colors you need to properly color the vertices of the graph. This is called the
chromatic number of the graph. Think about how you know your answer is correct.
Can you generalize? Can you conclude anything about the chromatic number for particular sorts of graphs?
