Related papers: Parameterizing Fullerenes with Vertex Combinations

We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of clusterings produced by running a clustering algorithm with…

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…

A fullerene graph is a cubic bridgeless plane graph with all faces of size 5 and 6. We show that that every fullerene graph on n vertices can be made bipartite by deleting at most sqrt{12n/5} edges, and has an independent set with at least…

This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We…

We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so…

A graph is said to be cyclic $k$-edge-connected, if at least $k$ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of $k$ edges is called a cyclic-$k$-edge cutset and it is called a trivial…

We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…

Finding clusters of well-connected nodes in a graph is an extensively studied problem in graph-based data analysis. Because of its many applications, a large number of distinct graph clustering objective functions and algorithms have…

A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$…

A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially…

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since…

We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…

Structural graph parameters play an important role in parameterized complexity, including in kernelization. Notably, vertex cover, neighborhood diversity, twin-cover, and modular-width have been studied extensively in the last few years.…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper we completely characterize the pairs (graph, matching complex) for…

We consider seven fundamental properties of cellular embeddings of graphs in compact surfaces, and show that each property can be associated with a point of the Fano plane $F$, in such a way that allowable combinations of properties…

Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…