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We show in this note that the average number of terms in the optimal double-base number system is in Omega(n / log n). The lower bound matches the upper bound shown earlier by Dimitrov, Imbert, and Mishra (Math. of Comp. 2008).
A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph $G$ contains a cactus subgraph $C$ where $C$ contains at least a $frac{1}{6}$ fraction of the triangular faces of $G
The view of a node in a port-labeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers $ngeq Dgeq 1$, there exists a port-labeled network with at most $n$ nodes and diameter at mo
In [13] the authors show that if $mu$ is a strongly compact cardinal, $K$ is an Abstract Elementary Class (AEC) with $LS(K)<mu$, and $K$ satisfies joint embedding (amalgamation) cofinally below $mu$, then $K$ satisfies joint embedding (amalgamation)
In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.
An interval edge t-coloring of a graph G is a proper edge coloring of G with colors 1,2...,t such that at least one edge of G is colored by color i,i=1,2...,t, and the edges incident with each vertex v are colored by d_{G}(v) consecutive colors, wher