Related papers: Online Edge Coloring via Tree Recurrences and Corr…
The problem of sampling edge-colorings of graphs with maximum degree $\Delta$ has received considerable attention and efficient algorithms are available when the number of colors is large enough with respect to $\Delta$. Vizing's theorem…
Consider the following simple coloring algorithm for a graph on $n$ vertices. Each vertex chooses a color from $\{1, \dotsc, \Delta(G) + 1\}$ uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at…
Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…
We present a simple randomized algorithm that can efficiently maintain a $(\Delta+1)$ coloring as the graph undergoes edge insertion and deletion updates, where $\Delta$ denotes an upper bound on the maximum degree. A key advantage is the…
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve…
In this paper we show that every graph $G$ of bounded maximum average degree ${\rm mad}(G)$ and with maximum degree $\Delta$ can be edge-colored using the optimal number of $\Delta$ colors in quasilinear time, whenever $\Delta\ge 2{\rm…
In this paper we present a deterministic CONGEST algorithm to compute an $O(k\Delta)$-vertex coloring in $O(\Delta/k)+\log^* n$ rounds, where $\Delta$ is the maximum degree of the network graph and $1\leq k\leq O(\Delta)$ can be freely…
We develop an improved bound for the chromatic number of graphs of maximum degree $\Delta$ under the assumption that the number of edges spanning any neighbourhood is at most $(1-\sigma)\binom{\Delta}{2}$ for some fixed $0<\sigma<1$. The…
In this paper, we present improved algorithms for the $(\Delta+1)$ (vertex) coloring problem in the Congested-Clique model of distributed computing. In this model, the input is a graph on $n$ nodes, initially each node knows only its…
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.…
Given a graph, an edge coloring assigns colors to edges so that no pairs of adjacent edges share the same color. We are interested in edge coloring algorithms under the W-streaming model. In this model, the algorithm does not have enough…
We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…
We propose a new proof technique that aims to be applied to the same problems as the Lov\'asz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve…
We study the edge-coloring problem in simple $n$-vertex $m$-edge graphs with maximum degree $\Delta$. This is one of the most classical and fundamental graph-algorithmic problems. Vizing's celebrated theorem provides…
The problem of coloring the edges of an $n$-node graph of maximum degree $\Delta$ with $2\Delta - 1$ colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of progress…
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…
The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…
Vizing's celebrated theorem states that every simple graph with maximum degree $\Delta$ admits a $(\Delta+1)$ edge coloring which can be found in $O(m \cdot n)$ time on $n$-vertex $m$-edge graphs. This is just one color more than the…
A repetition is a sequence of symbols in which the first half is the same as the second half. An edge-coloring of a graph is repetition-free or nonrepetitive if there is no path with a color pattern that is a repetition. The minimum number…
Given a graph $G$, an edge-coloring is an assignment of colors to edges of $G$ such that any two edges sharing an endpoint receive different colors. By Vizing's celebrated theorem, any graph of maximum degree $\Delta$ needs at least…