An integer analogue of Carathéodory's theorem

AbstractWe prove a theorem on Hilbert bases analogous to Carathéodory's theorem for convex cones. The result is used to give an upper bound on the number of nonzero variables needed in optimal solutions to integer programs associated with totally dual integral systems. For integer programs arising from perfect graphs the general bounds are improved to show that if G is a perfect graph with n nodes and w is a vector of integral node weights, then there exists a minimum w-covering of the nodes that uses at most n distinct cliques

Stable Set Bonding in Perfect Graphs and Parity Graphs

AbstractLet G1 = (V1 ∪ S1, E1) and G2 = (V2 ∪ S2, E2) be connected graphs which each have stable sets S1 (resp. S2) of the same size. Let ΦS be the operation which forms G = (V, E) from G1 and G2 by identification of S1 and S2, where S ⊆ V corresponds to S1 and S2. If all minimal chains in G1 and G2, linking v to w for v, w ∈ S have the same parity, and if H1 and H2 are parity graphs where G1 ΦSH2, H1 ΦSG2, and H1 ΦSH2 are perfect graphs then G1 ΦSG2, is also perfect. This leads to a new composition operation which preserves perfection

Arboricity, h-Index, and Dynamic Algorithms

In this paper we present a modification of a technique by Chiba and Nishizeki [Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J. Comput. 14(1), pp. 210--223 (1985)]. Based on it, we design a data structure suitable for dynamic graph algorithms. We employ the data structure to formulate new algorithms for several problems, including counting subgraphs of four vertices, recognition of diamond-free graphs, cop-win graphs and strongly chordal graphs, among others. We improve the time complexity for graphs with low arboricity or h-index.Comment: 19 pages, no figure

Claw-free t-perfect graphs can be recognised in polynomial time

A graph is called t-perfect if its stable set polytope is defined by non-negativity, edge and odd-cycle inequalities. We show that it can be decided in polynomial time whether a given claw-free graph is t-perfect

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

Lack of influence of the COX inhibitors metamizol and diclofenac on platelet GPIIb/IIIa and P-selectin expression in vitro

BACKGROUND: The effect of non-steroidal anti-inflammatory drugs (NSAIDs) for reduced platelet aggregation and thromboxane A(2 )synthesis has been well documented. However, the influence on platelet function is not fully explained. Aim of this study was to examine the influence of the COX-1 inhibiting NSAIDs, diclofenac and metamizol on platelet activation and leukocyte-platelet complexes, in vitro. Surface expression of GPIIb/IIIa and P-selectin on platelets, and the percentage of platelet-leukocyte complexes were investigated. METHODS: Whole blood was incubated with three different concentrations of diclofenac and metamizol for 5 and 30 minutes, followed by activation with TRAP-6 and ADP. Rates of GPIIb/IIIa and P-selectin expression, and the percentage of platelet-leukocyte complexes were analyzed by a flow-cytometric assay. RESULTS: There were no significant differences in the expression of GPIIb/IIIa and P-selectin, and in the formation of platelet-leukocyte complexes after activation with ADP and TRAP-6, regarding both the time of incubation and the concentrations of diclofenac and metamizol. CONCLUSIONS: Accordingly, the inhibitory effect of diclofenac and metamizol on platelet aggregation is not related to a reduced surface expression of P-selectin and GPIIb/IIIa on platelets