Weighted fractional and integral k-matching in hypergraphs

Weighted Fractional and Integral K-matching in Hypergraphs

Perfect Fractional Matchings in $k$-Out Hypergraphs

Extending the notion of (random) k-out graphs, we consider when the k-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each r there is a k = k(r) such that the k-out r-uniform hypergraph on n vertices has a perfect fractional matching with high probability (i.e., with probability tending to 1 as n → ∞) and prove an analogous result for r-uniform r-...

Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.

Sharp Weighted Bounds for Fractional Integral Operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal...

An algorithm for weighted fractional matroid matching

LetM be a matroid on ground set E. A subset l ⊆ E is called a line when r(l) ∈ {1, 2}. Given a set of lines L = {l1, . . . , lk} in M , a vector x ∈ RL+ is called a fractional matching when ∑ l∈L xla(F )l ≤ r(F ) for every flat F ofM . Here a(F )l is equal to 0 when l∩F = ∅, equal to 2 when l ⊆ F and equal to 1 otherwise. We refer to ∑ l∈L xl as the size of x. It was shown by Chang et al. that ...