In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirch...

We construct an infinite family of 3-manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots ( +1)2 or ( +1)1, that are the closure of the rational (2 −1)/( −1)–tangles or (2 −1)/ –tangles, respectively.

This paper presents our work on decomposing a specific nurse rostering problem by cyclically assigning blocks of shifts, which are designed considering both hard and soft constraints, to groups of nurses. The rest of the shifts are then assigned to the nurses to construct a schedule based on the one cyclically generated by blocks. The schedules obtained by decomposition and construction can be ...

We consider the following conjecture. Suppose that G is a non-free non-cyclic onerelator group such that each subgroup of finite index is again a one-relator group and each subgroup of infinite index is a free group. Must G be a surface group? We show that if G is a freely indecomposable fully residually free group and satisfies the property that every subgroup of infinite index is free then G ...