Related papers: Higher dimensional analogues of the map colouring …
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
We derive three-dimensional integrable mappings which have two invariants.
This paper introduces a novel method for image colorization that utilizes a color transformer and generative adversarial networks (GANs) to address the challenge of generating visually appealing colorized images. Conventional approaches…
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
Human beings can imagine the colours of a grayscale image with no particular effort thanks to their ability of semantic feature extraction. Can an autonomous system achieve that? Can it hallucinate plausible and vibrant colours? This is the…
Image forensics, aiming to ensure the authenticity of the image, has made great progress in dealing with common image manipulation such as copy-move, splicing, and inpainting in the past decades. However, only a few researchers pay…
In this article, we use a unified approach to prove several classes of planar graphs are DP-$3$-colorable, which extend the corresponding results on $3$-choosability.
We consider the Hadwiger-Nelson problem on the chromatic number of the plane under conditions of coloring a map containing a finite number of vertices in any bounded region. Woodall (1973) and Townsend (1981) showed that at least 6 colors…
DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvo\v{r}\'{a}k and Postle. Many known upper bounds for the list-chromatic number extend to the DP-chromatic number, but not all…
The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
In this paper, we introduce and study "geometric simultaneous RAC drawing problems", i.e., a combination of problems on geometric RAC drawings and geometric simultaneous graph drawings. To the best of our knowledge, this is the first time…
Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
We present the Douglas-Rachford algorithm as a successful heuristic for solving graph coloring problems. Given a set of colors, these type of problems consist in assigning a color to each node of a graph, in such a way that every pair of…
We aim at predicting a complete and high-resolution depth map from incomplete, sparse and noisy depth measurements. Existing methods handle this problem either by exploiting various regularizations on the depth maps directly or resorting to…
In many practical applications the underlying graph must be as equitable colored as possible. A coloring is called equitable if the number of vertices colored with each color differs by at most one, and the least number of colors for which…
Perfect colorings (equitable partitions) of graphs are extensively studied, while the same concept for hypergraphs attracts much less attention. The aim of this paper is to develop basic notions and properties of perfect colorings for…
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…