Some new results on k-free numbers

Some New Results on Policy Limit Allocations

Suppose that a policyholder faces $n$ risks X1, ..., Xn which are insured under the policy limit with the total limit of l. Usually, the policyholder is asked to protect each Xi with an arbitrary limit of li such that ∑ni=1li=l. If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, ...

Some New Results for k - Dense Trees

Some recent results on Ramsey-type numbers

In this paper we survey author’s recent results on quantitative extensions of Ramsey theory. In particular, we discuss our recent results on Folkman numbers, induced bipartite Ramsey graphs, and explicit constructions of Ramsey graphs.

Some Exact Results And New Asymptotics For Hypergraph Turán Numbers

Given a family F of r-graphs, let ex(n,F) be the maximum number of edges in an n vertex r-graph containing no member of F . Let C 4 denote the family of r-graphs with distinct edges A,B, C, D, such that A ∩ B = C ∩ D = ∅, A ∪ B = C ∪ D. For s1 ≤ · · · ≤ sr, let K(s1, . . . , sr) be the complete r-partite r-graph with parts of sizes s1, . . . , sr. Füredi conjectured over 15 years ago that ex(n,...

Some New Results On the Hosoya Polynomial of Graph Operations

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...