Sigma Partitioning: Complexity and Random Graphs
A $ extit{sigma partitioning}$ of a graph $G$ is a partition of the vertices into sets $P_1, ldots, P_k$ such that for every two adjacent vertices $u$ and $v$ Hobby Paint there is an index $i$ such that $u$ and $v$ have different numbers of neighbors in $P_i$.The $ extit{ sigma number}$ of a graph $G$, denoted by $sigma(G)$, is the minimum number $