m$-$Coloring Problem: Given m colors c$1,$ c$2,...,$ cm$,$ and an undirected graph G$($V$,$E$)$ we seek to assign a color to each vertex in V such that for any edge $($u$,$v$)$

E$,$ u and v are assigned different colors. Is the graph G m$-$colorable? If yes, then return the color of each vertex. If not, then return a message "The graph cannot be m$-$colored".

Design a backtracking algorithm to solve the m$-$coloring problem using the general framework discussed in class. All other solutions will not receive credit.

$//$define variables used

coloring$($m$,$ G$)$

$//$ add your pseudocode here

r$-$coloring$($k$,$ m$,$ G$)$

$//$add your pseudocode here

color$\_$ok$($k$,$ G$)$

$//$add your pseudocode here

Write the pseudo$-$code

Analyze the worst$-$case running time of your algorithm.