Balanced minimum covers of a finite set

A minimum data set for chronic venous disease

Approximating set multi-covers

Lovász and Stein (independently) proved that any hypergraph satisfies τ ≤ (1+ln ∆)τ * , where τ is the transversal number, τ * is its fractional version, and ∆ denotes the maximum degree. We prove τ f ≤ 3.17τ * max{ln ∆, f } for the f-fold transversal number τ f. Similarly to Lovász and Stein, we also show that this bound can be achieved non-probabilistically, using a greedy algorithm. As a com...

Diameter Two Graphs of Minimum Order with Given Degree Set

The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

Almost-free finite covers

Let W be a first-order structure and ρ be an Aut(W )-congruence on W . In this paper we define the almost-free finite covers of W with respect to ρ, and we show how to construct them. These are a generalization of free finite covers. A consequence of a result of [5] is that any finite cover of W with binding groups all equal to a simple non-abelian permutation group is almostfree with respect t...

Approximability of Minimum-weight Cycle Covers

A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N. For most sets L, computing L-cycle covers of minimum weight is NP-hard and APX-hard. While computing L-cycle covers of maximum weight admits constant factor approximation algorithms (both for undirected and dir...