Strong coloring

When the order of the graph G is not divisible by k, we add isolated vertices to G just enough to make the order of the new graph G′ divisible by k. In that case, a strong coloring of G′ minus the previously added isolated vertices is considered a strong coloring of G. [1] The strong chromatic number sχ(G) of a graph G is the least k such that G is strongly k-colorable.

Strong chromatic number was independently introduced by Alon (1988)[4][5] and Fellows (1990).

This is in contrast to graph coloring, which is a partition of the vertices of a graph into a given number of independent sets, without the requirement that these independent sets be transversals.

But some faculty members are in conflict and will not sit in the same committee.

If the "conflict" relations are represented by the edges of a graph, then:

This Möbius ladder is strongly 4-colorable. There are 35 4-sized partitions, but only these 7 partitions are topologically distinct.