相关论文: The Generation of Fullerenes

Considering regions in a map to be adjacent when they have nonempty intersection (as opposed to the traditional view requiring intersection in a linear segment) leads to the concept of a facially complete graph: a plane graph that becomes…

Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such…

The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2. We find that there are no fullerenes whose…

We introduce new and simple algorithms for the calculation of the number of perfect matchings of complex weighted, undirected graphs with and without loops. Our compact formulas for the hafnian and loop hafnian of $n \times n $ complex…

Barnette's conjecture states that every cubic, bipartite, planar and 3-connected graph is Hamiltonian. Goodey verified Barnette's conjecture for all graphs with faces of size up to 6. We substantially strengthen Goodey's result by proving…

We develop a new method that improves the efficiency of equation-by-equation algorithms for solving polynomial systems. Our method is based on a novel geometric construction, and reduces the total number of homotopy paths that must be…

Given a set of $m$ points and a set of $n$ lines in the plane, we consider the problem of computing the faces of the arrangement of the lines that contain at least one point. In this paper, we present an $O(m^{2/3}n^{2/3}+(n+m)\log n)$ time…

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse…

Accurate and fast recognition of forgeries is an issue of great importance in the fields of artificial intelligence, image processing and object detection. Recognition of forgeries of facial imagery is the process of classifying and…

Massive power-law graphs drive many fields: metagenomics, brain mapping, Internet-of-things, cybersecurity, and sparse machine learning. The development of novel algorithms and systems to process these data requires the design, generation,…

Barnette's conjecture asserts that every cubic $3$-connected plane bipartite graph is hamiltonian. Although, in general, the problem is still open, some partial results are known. In particular, let us call a face of a plane graph big…

Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview…

We present a novel approach to the age-old question of whether perfect cuboids exist. Our approach consists of two new computer search algorithms, arising from the analysis of "perfect plinths" reported by one of us recently, that are much…

There are many representations of planar graphs, but few are as elegant as Tur\'an's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main…

We show a kernel of at most $13k$ vertices for the Planar Feedback Vertex Set problem restricted to planar graphs, i.e., a polynomial-time algorithm that transforms an input instance $(G,k)$ to an equivalent instance with at most $13k$…

We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zonotope's vertices by sampling a random linear combination of…

In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…

This article introduces new algorithms for the uniform random generation of labelled planar graphs. Its principles rely on Boltzmann samplers, as recently developed by Duchon, Flajolet, Louchard, and Schaeffer. It combines the Boltzmann…

Synthetic polymeric materials underpin fundamental technologies in the energy, electronics, consumer goods, and medical sectors, yet their development still suffers from prolonged design timelines. Although polymer informatics tools have…

The cage problem concerns finding $(k,g)$-graphs, which are $k$-regular graphs with girth $g$, of the smallest possible number of vertices. The central goal is to determine $n(k,g)$, the minimum order of such a graph, and to identify…