Conditional and Unique Coloring of Graphs

P. Venkata Subba Reddy, K. Viswanathan Iyer

For integers $k,r>0$, a conditional $(k,r)$-coloring of a graph $G$ is a proper $k$-coloring of the vertices of $G$ such that every vertex $v$ of degree $d(v)$ in $G$ is adjacen…