
A labeling of the vertices of a graph with distinct natural numbers induces a natural labeling of its edges: the label of an edge
The method of large scale group testing has been used in the economical testing of blood samples, and in non-testing situations such as experimental designs and coding theory, for over 50 years. Some very basic questions addressing the minimum number of tests required to identify defective samples still remain unsolved, including the situation where one defective sample in each of two batches are to be found. This gives rise to an intriguing graph theoretical conjecture concerning bipartite graphs, a conjecture which in this paper is proved to be true in the case where vertices in one part of the bipartite graph have low degree.
Using the action of the linear fractional groups
Here we consider string matching problems that arise naturally in applications to music retrieval. The
In 2004, Kim and Nakprasit showed that the chromatic number of
Let
In this paper we find ten new weighing matrices of order
A dominating set
Let
The Hamilton-Waterloo problem in the case of triangle-factors and Hamilton cycles asks for a
There exist
Chessboard separation problems are modifications to classic chessboard problems, such as the
In this paper, it is shown that the graph obtained by overlapping the cycle
A graph
The chromatic polynomial of a graph
The
Let
For two vertices
For a vertex
In this paper, we consider the non-existence of some bi-level orthogonal arrays (O-arrays) of strength six, with
We present constructions and results about GDDs with two groups and block size five in which each block has configuration
The covering number for a subset of leaves in a finite rooted tree is defined as the number of subtrees that remain after deleting all the paths connecting the root to the other leaves. We find the formula for the total sum (hence the average) of the covering numbers for a given subset of labeled leaves over all unordered binary trees with
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