A vertex cover CsubeV of an undirected graph $G=(V,E)$ is a set such that

$|eC|1$

for every einE, i$.$e$.,$ if $ij$ in $E$ then iinC or jinC $($or both$).$

$($a$)$ Show that the following decision problem is $NP-$complete by reduction to

STAB$-$d $($as defined in class$)$:

VERTEX$-$COVER$-$d $($VC$-$d$)$: Given an undirected graph $G=(V,E)$ and

integer $L,$ does $G$ contain a vertex cover of size $|C|L?$