Related papers: Random Graph Coloring - a Statistical Physics Appr…
The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for…
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
A {\bf $\mathbf{k}$-majority coloring} of a digraph $D=(V,A)$ is a coloring of $V$ with $k$ colors so that each vertex $v\in V$ has at least as many out-neighbours of color different from its own color as it has out-neighbours with the same…
Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study…
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…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…
NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a…
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…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
A vertex colouring of a given graph $G$ can be considered as a random experiment. A discrete random variable $X$, corresponding to this random experiment, can be defined as the colour of a randomly chosen vertex of $G$ and a probability…
A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
A simple but empirically efficient heuristic algorithm for the edge-coloring of graphs is presented. Its basic idea is the displacement of "conflicts" (repeated colors in the edges incident to a vertex) along paths of adjacent vertices…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
We study the problem of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted a lot of attention. For list packing the setup is similar but we seek a…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
We develop a heuristic graph coloring approximation algorithm that uses the D-Wave 2X as an independent set sampler and evaluate its performance against a fully classical implementation. A randomly generated set of small but hard graph…
For graph classes $P_1,...,P_k$, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph $G$ can be partitioned into subsets $V_1,...,V_k$ so that $V_j$ induces a graph in the class $P_j$…