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In the paper we consider the problem of scheduling $n$ identical jobs on 3uniform machines with speeds $s_1, s_2,$ and $s_3$ to minimize the schedulelength. We assume that jobs are subjected to some kind of mutual exclusionconstraints, modeled by a cubic incompatibility graph. We show that if thegraph is 2-chromatic then the problem can be solved in $O(n^2)$ time. If thegraph is 3-chromatic, the problem becomes NP-hard even if $s_1>s_2=s_3$.However, in this case there exists a $4/3$-approximation algorithm running in$O(n^3)$ time. Moreover, this algorithm solves the problem almost surely tooptimality if $3s_1/4 \leq s_2 = s_3$.

Scheduling of unit-length jobs with cubic incompatibility graphs on three uniform machines