Related papers: Higher dimensional analogues of the map colouring …
This paper discusses reformulations of the problem of coloring plane maps with four colors. The context is the edge-coloring with three colors of cubic graphs such that three distinct colors occur at each vertex. We include discussion of…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
The DP-coloring problem is a generalization of the list-coloring problem in which the goal is to find an independent transversal in a certain topological cover of a graph $G$. In the online DP-coloring problem, the cover of $G$ is revealed…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
In recent years, the field of image inpainting has developed rapidly, learning based approaches show impressive results in the task of filling missing parts in an image. But most deep methods are strongly tied to the resolution of the…
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…
We establish closed-form expansions for the number of colorings of a path or cycle on n vertices with colors from 1,...,x such that adjacent vertices are colored differently or with colors from y+1,...x.
We study the problem of colouring visibility graphs of polygons. In particular, for visibility graphs of simple polygons, we provide a polynomial algorithm for 4-colouring, and prove that the 5-colourability question is already NP-complete…
We prove a better coloring theorem for aleph_4 and even aleph_3. This has a general topology consequence.
Image colorization is a challenging problem due to multi-modal uncertainty and high ill-posedness. Directly training a deep neural network usually leads to incorrect semantic colors and low color richness. While transformer-based methods…
Colorization of gray-scale images relies on prior color information. Examplar-based methods use a color image as source of such information. Then the colors of the source image are transferred to the gray-scale image. In the literature,…
Homographies -- a mathematical formalism for relating image points across different camera viewpoints -- are at the foundations of geometric methods in computer vision and are used in geometric camera calibration, image registration, and…
In the Coloured Clustering problem, we wish to colour vertices of an edge coloured graph to produce as many stable edges as possible, i.e., edges with the same colour as their ends. In this paper, we reveal that the problem is in fact a…
One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
We consider vertex coloring of an acyclic digraph $\Gdag$ in such a way that two vertices which have a common ancestor in $\Gdag$ receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data…
Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that $\frac32\Delta+1$ colors are sufficient…
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:…
A lower bound is obtained for the greatest possible number of colors in an interval colourings of some regular graphs.
Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not "under control" from a polyhedral point of view. The equivalence between \emph{optimization} and…
We consider the polychromatic coloring problems for unions of two or more geometric hypergraphs on the same vertex sets of points in the plane. We show, inter alia, that the union of bottomless rectangles and horizontal strips does in…