We prove that the property of containing a k-regular subgraph in the random graph model G(n, p) has a sharp threshold for k ≥ 3. We also show how to use similar methods to obtain an easy prove for the (known fact of) sharpness of having a non empty k-core for k ≥ 3.

In Australia, as in other comparable countries, the link between heroin addiction and acquisitive crime has been well documented. Around 40% of males incarcerated in Long Bay Gaol for property offences report having used heroin (Dobinson and Ward, 1985), indicating that heroin use is far more common in this group than in community samples, in which reported rates of ever having used heroin are ...

‎a new method for the defuzzification of fuzzy numbers is developed in this paper. it is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. but different fuzzy numbers are often converted into one crisp number. in this case the loss of essential information is possible. it may result in inadequate final conclusions, for example, expert...