The chromatic number has a well-known interpretation in the area of scheduling. If the vertices of a finite, simple graph are committees, and adjacency of two committees indicates that they must never be in session simultaneously, then the chromatic number of the graph is the smallest number of hours during which the committees/vertices of the graph may all have properly scheduled meetings of one continuous hour each. Slivnik  showed that the fractional chromatic number can be similarly characterized. In that characterization, the meetings are allowed to be broken into a finite number of disjoint intervals. Here we consider chromatic numbers definable similarly, with the additional restriction that there are only k meeting rooms available; that is, at each instant no more than k committees can be in session.
Johnson, Peter and Zha, Xiaoya
"Scheduling N Burgers for a k-Burger Grill: Chromatic Numbers With Restrictions,"
Theory and Applications of Graphs: Vol. 2
, Article 3.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol2/iss2/3