CONSTRAINED PARTITIONING PROBLEMS

Burkard and Yao studied matroid-constrained optimal partitioning probl ems and developed an algorithm for determining optimal partitions. Cru cial to their development is the property that pairwise consecutivenes s implies consecutiveness, and they observed that this implication hol ds under the assumption that no loops are present in the underlying ma troids. Here, we provide an example that demonstrates that the implica tion need not hold in general. We also present an alternative sufficie nt condition under which the implication is valid regardless of the pr esence of loops.