Related papers: Distributed Colour Reduction Revisited

We propose a new algorithm for 3-coloring that runs in time O(1.3217^n). For this algorithm, we make use of the time O(1.3289^n) algorithm for 3-coloring by Beigel and Eppstein. They described a structure in all graphs, whose vertices could…

In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by…

We show that there is a one-round randomized distributed algorithm that can 2-color cycles such that the expected fraction of monochromatic edges is less than 0.24118. We also show that a one-round algorithm cannot achieve a fraction less…

In this paper, we give a polynomial time algorithm which determines if a given graph containing a triangle and no induced seven-vertex path is 3-colorable, and gives an explicit coloring if one exists. In previous work, we gave a polynomial…

We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel…

A {\it dynamic $k$-coloring} of a graph $G$ is a proper $k$-coloring of the vertices of $G$ such that every vertex of degree at least 2 in $G$ will be adjacent to vertices with at least 2 different colors. The smallest number $k$ for which…

List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…

Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…

We present a randomized distributed algorithm that computes a $\Delta$-coloring in any non-complete graph with maximum degree $\Delta \geq 4$ in $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$ rounds, as well as a randomized algorithm that…

The asymmetric coloring number of a graph is the minimum number of colors needed to color its vertices, so that no non-trivial automorphism preserves the color classes. We investigate the asymmetric coloring number of graphs that are…

We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph's arboricity, $\alpha$. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm…

The distributed (Delta + 1)-coloring problem is one of most fundamental and well-studied problems of Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms…

A planar graph can be embedded in a piecewise linear manifold, and the lattice on each linear piece can be colored with 3-coloring. If a planar graph can be colored with multiple 3-coloring, i.e. coloring the graph in pieces with different…

The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a…

We consider the problem of maintaining a proper $(\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time…

Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…

We present a deterministic distributed algorithm, in the LOCAL model, that computes a $(1+o(1))\Delta$-edge-coloring in polylogarithmic-time, so long as the maximum degree $\Delta=\tilde{\Omega}(\log n)$. For smaller $\Delta$, we give a…

We consider a decentralized graph coloring model where each vertex only knows its own color and whether some neighbor has the same color as it. The networking community has studied this model extensively due to its applications to channel…

We present a new technique to efficiently sample and communicate a large number of elements from a distributed sampling space. When used in the context of a recent LOCAL algorithm for $(\operatorname{degree}+1)$-list-coloring (D1LC), this…

Graph colorings is a fundamental topic in graph theory that require an assignment of labels (or colors) to vertices or edges subject to various constraints. We focus on the harmonious coloring of a graph, which is a proper vertex coloring…