We obtain \(135\) nonisomorphic nearly Kirkman triple systems of order \(18\) (the smallest order for which such a system exists), including all \(119\) systems of a well-defined subclass.

In overloaded task systems, it is by definition not possible to complete all tasks by their deadlines. However, it may still be desirable to maximize the number of in-time task completions. The performance of on-line schedulers with respect to this metric is investigated here. It is shown that in general, an on-line algorithm may perform arbitrarily poorly as compared to clairvoyant (off-line) schedulers. This result holds for general task workloads where there are no constraints on task characteristics. For a variety of constrained workloads that are representative of many practical applications, however, on-line schedulers that do provide a guaranteed level of performance are presented.

We present a new algorithm for computer searches for orthogonal designs. Then we use this algorithm to find new sets of sequences with entries from \(\{0,\pm a, \pm b, \pm c,\pm d\}\) on the commuting variables \(a, b, c, d\) with zero autocorrelation function.

Consider the hit polynomial of the path \(P_{2n}\) embedded in the complete graph \(K_{2n}\). We give a combinatorial interpretation of the \(n\)-th Bessel polynomial in terms of a modification of this hit polynomial, called the ordered hit polynomial. Also, the first derivative of the \(n\)-th Bessel polynomial is shown to be the ordered hit polynomial of \(P_{2n-1}\) embedded in \(K_{2n}\).

In a packer-spoiler game on a graph, two players jointly construct a maximal partial \(F\)-packing of the graph according to some rules, where \(F\) is some given graph. The packer wins if all the edges are used up and the spoiler wins otherwise. The question of which graphs are wins for which player generalizes the questions of which graphs are \(F\)-packable and which are randomly \(F\)-packable. While in general such games are NP-hard to solve, we provide partial results for \(F = P_3\) and solutions for \(F = 2K_2\).

Let G be a \((p,q)\)-graph with p vertices and q edges. An edge-labeling assignment \(\text{L : E} \to \text{N}\) is a map which assigns a positive integer to each edge in E. The induced map \(\text{L}^+ : \text{V} \to \text{N}\) defined by \(\text{L}^+\text{(v)} = \Sigma\{\text{L(u,v) : for all (u,v) in E}\}\) is called the vertex sum. The edge labeling assignment is called \underline{magic} if \(\text{L}^+\) is a constant map. If L is a bijection with \(\text{L(E)} = \{1,2,\ldots,\text{q}\}\) and L is magic then we say L is supermagic. B. M. Stewart showed that \(\text{K}_5\) is not supermagic and when \(\text{n} \equiv 0 \pmod{4}\) , \(\text{K}_\text{n}\) is not supermagic. In this paper, we exhibit supermagicness for a class of regular complete k-partite graphs.