Related papers: Canonical Representations for Circular-Arc Graphs …
In this paper we propose an approach to investigate the canonical rings of surfaces of general type whose canonical system has isolated base points and yields a birational map onto its image. We apply then the method in the concrete case of…
We construct a polynomial-time algorithm that given a graph $X$ with $4p$ vertices ($p$ is prime), finds (if any) a Cayley representation of $X$ over the group $C_2\times C_2\times C_p$. This result, together with the known similar result…
We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an…
Recent developments in regularized Canonical Correlation Analysis (CCA) promise powerful methods for high-dimensional, multiview data analysis. However, justifying the structural assumptions behind many popular approaches remains a…
We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows.…
Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…
We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…
We use methods of the general theory of congruence and *congruence for complex matrices--regularization and cosquares-to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices…
Given the collection of all $m\times n$ rectangular grids which have a fixed number $1\leq r\leq mn$ of blocked cells, we explicitly describe a proper subset of the collection which is guaranteed to contain at least one grid from each…
A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…
In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of…
Building on the limit theory for set functions, we prove that the limit of convergent sequence of bounded-degree graphs' cycle matroids can be represented as the cycle matroid of a graphing, analogous to the completeness result for…
Modern vision pipelines increasingly rely on pretrained image encoders whose representations are reused across tasks and models, yet these representations are often overcomplete and model-specific. We propose a simple, training-free method…
Community detection in graphs is a problem that is likely to be relevant whenever network data appears, and consequently the problem has received much attention with many different methods and algorithms applied. However, many of these…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
In this paper, we investigate the importance of column scaling in relating two signed-graphic representations of the same matroid. We used the Sage Mathematics software to generate many examples of signed-graphic matroids and their…