A min-max theorem on tournaments

We present a structural characterization of all tournaments T = (V, A) such that, for any nonnegative integral weight function defined on V, the maximum size of a feedback vertex set packing is equal to the minimum weight of a triangle in T. We also answer a question of Frank by showing that it is N P-complete to decide whether the vertex set of a given tournament can be partitioned into two feedback vertex sets. In addition, we give exact and approximation algorithms for the feedback vertex set packing problem on tournaments. ©2007 Society for Industrial and Applied Mathematics.published_or_final_versio

An Optimal Binding Number Condition for Bipancyclism

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The Maximum-Weight Stable Matching Problem: Duality and Efficiency

Given a preference system (G,≺) and an integral weight function defined on the edge set of G (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of (G,≺) with maximum total weight. In this paper we study this NP-hard problem using linear programming and polyhedral approaches. We show that the Rothblum system for defining the fractional stable matching polytope of (G,≺) is totally dual integral if and only if this polytope is integral if and only if (G,≺) has a bipartite representation. We also present a combinatorial polynomial-time algorithm for the maximum-weight stable matching problem and its dual on any preference system with a bipartite representation. Our results generalize Király and Pap's theorem on the maximum-weight stable-marriage problem and rely heavily on their work. © 2012 Society for Industrial and Applied Mathematics.published_or_final_versio

3-(Pyridin-4-ylmeth­oxy)phenol

In the title compound, C12H11NO2, the phenolic ring is inclined at an angle of 32.70 (1)° with respect to the pyridine ring. In the crystal, inter­molecular O—H⋯N hydrogen bonds link the mol­ecules into C(11) chains along [001]

Deep3DSketch+: Obtaining Customized 3D Model by Single Free-Hand Sketch through Deep Learning

As 3D models become critical in today's manufacturing and product design, conventional 3D modeling approaches based on Computer-Aided Design (CAD) are labor-intensive, time-consuming, and have high demands on the creators. This work aims to introduce an alternative approach to 3D modeling by utilizing free-hand sketches to obtain desired 3D models. We introduce Deep3DSketch+, which is a deep-learning algorithm that takes the input of a single free-hand sketch and produces a complete and high-fidelity model that matches the sketch input. The neural network has view- and structural-awareness enabled by a Shape Discriminator (SD) and a Stroke Enhancement Module (SEM), which overcomes the limitations of sparsity and ambiguity of the sketches. The network design also brings high robustness to partial sketch input in industrial applications.Our approach has undergone extensive experiments, demonstrating its state-of-the-art (SOTA) performance on both synthetic and real-world datasets. These results validate the effectiveness and superiority of our method compared to existing techniques. We have demonstrated the conversion of free-hand sketches into physical 3D objects using additive manufacturing. We believe that our approach has the potential to accelerate product design and democratize customized manufacturing

catena-Poly[[[aqua­(pyridine-4-carboxyl­ato-κN)silver(I)]-μ-hexa­methyl­ene­tetra­amine-κ2 N:N′] dihydrate]

In the title compound, {[Ag(C6H4NO2)(C6H12N4)(H2O)]·2H2O}n, the AgI atom shows a distorted triangular pyramidal geometry,, formed by two N atoms from two hexa­methyl­ene­tetra­amine (hmt) ligands and one N atom from a pyridine-4-carboxyl­ate (4-pdc) ligand and one water mol­ecule. The hmt ligands bridge the Ag atoms, forming a chain along [001]. The carboxyl­ate group of the 4-pdc ligand is uncoordinated. O—H⋯O hydrogen bonds between the water mol­ecules and carboxyl­ate groups stabilize the structure

catena-Poly[[tris[silver(I)-μ-4,4′-bi­pyridine-κ2 N:N′]] tris­(perchlorate) di­hydrate]

In the title compound, {[Ag3(C10H8N2)3](ClO4)3·2H2O}n, one of the AgI ions, one of the 4,4′-bipyridine (bipy) ligands and one of the perchlorate anions are each situated on a twofold rotation axis. Each AgI ion is coordinated by two N atoms from two bridging bipy ligands, forming chains along [101]. π–π inter­actions between the pyridine rings [centroid–centroid distances = 3.638 (8) and 3.688 (8) Å] connect the chains. Inter­molecular O—H⋯O hydrogen bonds link the uncoord­inated water mol­ecules and the perchlorate anions