
We give a necessary and sufficient condition of Hall’s type for a family of sets of even cardinality to be decomposable into two subfamilies having a common system of distinct representatives. An application of this result to partitions of Steiner Triple Systems into small configurations is presented.
In this paper, we construct 2-factorizations of
We deal with
Let
A cycle
In an earlier paper [11], we proved that there does not exist any
In this paper, uniquely list colorable graphs are studied. A graph
A labeling
A graph
In this paper, we proved that the corona graph
In this paper, we derive a necessary existence condition involving the parameters of a balanced array (B-array) with two symbols and of strength
A set of
We conclude with the statement of a number of conjectures regarding some open questions.
We prove that if
The quantity
A set of edges
Let
Let
Let
Summary. In this paper, we present some inequalities on balanced arrays ({B-arrays}) of strength five with two symbols.
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