Related papers: Higher dimensional analogues of the map colouring …

Suppose that $nk$ points in general position in the plane are colored red and blue, with at least $n$ points of each color. We show that then there exist $n$ pairwise disjoint convex sets, each of them containing $k$ of the points, and each…

A c-coloring of G(n,m)=n x m is a mapping of G(n,m) into {1,...,c} such that no four corners forming a rectangle have the same color. In 2009 a challenge was proposed via the internet to find a 4-coloring of G(17,17). This attracted…

We study the behavior of the Douglas-Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In…

The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…

We study several basic problems about colouring the $p$-random subgraph $G_p$ of an arbitrary graph $G$, focusing primarily on the chromatic number and colouring number of $G_p$. In particular, we show that there exist infinitely many…

Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…

We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking on generic and ill-conditioned problems, as well as as…

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…

Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…

A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and…

We prove several results about the complexity of the role colouring problem. A role colouring of a graph $G$ is an assignment of colours to the vertices of $G$ such that two vertices of the same colour have identical sets of colours in…

The attempts to prove the Four Color Problem last for long years. A little hope arises that the properties of the minimal partial triangulations will be very useful for the solution of the Four Color Problem. That is why the material of…

We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum…

The project has carried out the re-optimization of image coloring in accordance with the existing Autocolorization direction model DDColor. For the experiments on the existing weights of DDColor, we found that it has limitations in some…

We propose a set of questions on the dynamics of H\'enon maps from the real, complex, algebraic and arithmetic points of view.

We propose a new algorithm for color transfer between images that have perceptually similar semantic structures. We aim to achieve a more accurate color transfer that leverages semantically-meaningful dense correspondence between images. To…

The broadcast scheduling problem asks how a multihop network of broadcast transceivers operating on a shared medium may share the medium in such a way that communication over the entire network is possible. This can be naturally modeled as…

In this paper, we give a family of online algorithms for the classical coloring problem of intersection graphs of discs with bounded diameter. Our algorithms make use of a geometric representation of such graphs and are inspired by an…

Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…

We investigate the possibility of proving upper bounds on Hadwiger's number of a graph with partial information, mirroring several known upper bounds for the chromatic number. For each such bound we determine whether the corresponding bound…