What is the chromatic number of the following graph?
some actual colouring :p
The chromatic number of a graph is the smallest number of colors needed to color the vertices so that no two adjacent vertices share the same color.
Hence minimum number of colors needed to color given graph is equal to $3$
For odd length cycles we need minimum $3$ colors for vertex coloring and for even length cycles we need just $2$.
Answer is $B$
The Four Color theorem
The chromatic number of a planar graph is no greater than four.
Using this we can rule out some option directly.
For odd length cycles we need minimum 3 colors for vertex coloring and for even length cycles we need just 2.
How is this information used to solve the given question ? Can someone elaborate on it ?
So 3 color used hence chromatic number =3 option B