Phylogenetic tree reconstruction requires construction of a multiple sequence alignment (MSA) from sequences. Computationally, it is difficult to achieve an optimal MSA for many sequences. Moreover, even if an optimal MSA is obtained, it may not be the true MSA that reflects the evolutionary history of the underlying sequences. Therefore, errors can be introduced during MSA construction which i...

Let G = (V, E) be a graph. A subset D of V is called common neighbourhood dominating set (CN-dominating set) if for every v ∈ V −D there exists a vertex u ∈ D such that uv ∈ E(G) and |Γ(u, v)| > 1, where |Γ(u, v)| is the number of common neighbourhood between the vertices u and v. The minimum cardinality of such CN-dominating set denoted by γcn(G) and is called common neighbourhood domination n...

The classical hypergraph Ramsey number rk(s, n) is the minimum N such that for every redblue coloring of the k-tuples of {1, . . . , N}, there are s integers such that every k-tuple among them is red, or n integers such that every k-tuple among them is blue. We survey a variety of problems and results in hypergraph Ramsey theory that have grown out of understanding the quantitative aspects of r...

Abstract. We discuss in some detail the general problem of computing averages of convergent Euler products, and apply this to examples arising from singular series for the k-tuple conjecture and more general problems of polynomial representation of primes. We show that the “singular series” for the k-tuple conjecture have a limiting distribution when taken over k-tuples with (distinct) entries ...

A Roman dominating function (RDF) on a digraph $D$ is a function $f: V(D)rightarrow {0,1,2}$ satisfying the condition that every vertex $v$ with $f(v)=0$ has an in-neighbor $u$ with $f(u)=2$. The weight of an RDF $f$ is the value $sum_{vin V(D)}f(v)$. The Roman domination number of a digraph $D$ is the minimum weight of an RDF on $D$. A set ${f_1,f_2,dots,f_d}$ of Roman dominating functions on ...