Related papers: On the Descriptive Complexity of Color Coding
We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This…
The curling number of a graph G is defined as the number of times an element in the degree sequence of G appears the maximum. Graph colouring is an assignment of colours, labels or weights to the vertices or edges of a graph. A colouring…
The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes -- a purely combinatorial one and two geometric ones. It is shown, that most…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
The coloring problem is studied in the paper for graph classes defined by two small forbidden induced subgraphs. We prove some sufficient conditions for effective solvability of the problem in such classes. As their corollary we determine…
We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We…
More than ten years ago in 2008, a new kind of graph coloring appeared in graph theory, which is the {\it rainbow connection coloring} of graphs, and then followed by some other new concepts of graph colorings, such as {\it proper…
Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…
The packing coloring problem has diverse applications, including frequency assignment in wireless networks, resource distribution and facility location in smart cities and post-disaster management, as well as in biological diversity.…
Computing the smallest number $q$ such that the vertices of a given graph can be properly $q$-colored is one of the oldest and most fundamental problems in combinatorial optimization. The $q$-Coloring problem has been studied intensively…
Color constancy is the problem of inferring the color of the light that illuminated a scene, usually so that the illumination color can be removed. Because this problem is underconstrained, it is often solved by modeling the statistical…
Descriptive complexity theory is an important area in the study of computational complexity. In this direction, it is possible to describe combinatorial problems exclusively by logical methods, without resorting to the use of complicated…
Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…
The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…
Image colorization aims to bring colors back to grayscale images. Automatic image colorization methods, which requires no additional guidance, struggle to generate high-quality images due to color ambiguity, and provides limited user…
Visualizations often encode numeric data using sequential and diverging color ramps. Effective ramps use colors that are sufficiently discriminable, align well with the data, and are aesthetically pleasing. Designers rely on years of…
Image colorization adds color to grayscale images. It not only increases the visual appeal of grayscale images, but also enriches the information contained in scientific images that lack color information. Most existing methods of…
In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit…
The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a…
Over the last decades, hand-crafted feature extractors have been used to encode image visual properties into feature vectors. Recently, data-driven feature learning approaches have been successfully explored as alternatives for producing…