Block‐avoiding point sequencings

Sequencings and Howell Designs

Gracefulness, Group Sequencings and Graph Factorizations

In this article we survey recent results on the connection between decompositions of complete graphs which admit given automorphism groups, and some combinatorial problems related to these groups. Although these problems are of combinatorial nature, group theorists may find interest in these problems as well. Most of the results surveyed here are found in [10], [11], [12] and [14] (we do not gi...

Regular Oberwolfach Problems and Group Sequencings

We deal with Oberwolfach factorizations of the complete graphs Kn and K n *, which admit a regular group of automorphisms. We show that the existence of such a factorization is equivalent to the existence of a certain difference sequence defined on the elements of the automorphism group, or to a certain sequencing of the elements of that group. In the particular case of a hamiltonian factorizat...

R-sequencings and strong half-cycles from narcissistic terraces

We construct narcissistic terraces for cyclic groups that have various properties which enable the construction of R-sequencings and strong halfcycles for many non-cyclic abelian groups. Among other results, we show: that an abelian group which is isomorphic to a direct product of cyclic factors such that the number of factors of order congruent to 3 (mod 4) of order at most 79 is at least as l...

Transitive large sets of disjoint decompositions and group sequencings

Let n¿ 3 be an integer, and let k denote either n or n − 1. A large set of disjoint decompositions of K∗ n (Kn) into cycles of length k (denoted by k-LSD), is a partition of the set of all cycles of length k in K∗ n (Kn) into disjoint decompositions of K ∗ n (Kn) (i.e., any two decompositions have no k-cycle in common). Such a large set is transitive, if there exists a permutation group on the ...