相关论文: Contains and Inside relationships within combinato…

A hypermap is an embedding of a connected hypergraph into an orientable closed surface. A covering between hypermaps is a homomorphism between the embedded hypergraphs which extends to an orientation-preserving covering of the supporting…

In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze…

We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…

A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…

A locally irregular graph is a graph whose adjacent vertices have distinct degrees, a regular graph is a graph where each vertex has the same degree and a locally regular graph is a graph where for every two adjacent vertices u, v, their…

The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent…

Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…

Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biology. We develop a formal theory of cogs and establish a…

Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…

Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…

Multi-robot systems of increasing size and complexity are used to solve large-scale problems, such as area exploration and search and rescue. A key decision in human-robot teaming is dividing a multi-robot system into teams to address…

On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are…

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles…

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…

We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related to each other through regular coverings and parallel…

A graph is called pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this…

Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…