Locality in distributed graph algorithms
SIAM Journal on Computing
On the complexity of distributed network decomposition
Journal of Algorithms
Coloring graphs with sparse neighborhoods
Journal of Combinatorial Theory Series B
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Fast distributed algorithms for Brooks-Vizing colorings
Journal of Algorithms
Asymptotically the list colouring constants are 1
Journal of Combinatorial Theory Series B
A General Upper Bound on the List Chromatic Number of Locally Sparse Graphs
Combinatorics, Probability and Computing
A Note on Vertex List Colouring
Combinatorics, Probability and Computing
Journal of Graph Theory
Distributed (δ+1)-coloring in linear (in δ) time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weak graph colorings: distributed algorithms and applications
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
A new technique for distributed symmetry breaking
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
An algorithmic approach to the lovász local lemma. I
Random Structures & Algorithms
The Locality of Distributed Symmetry Breaking
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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Vertex coloring is a central concept in graph theory and an important symmetry-breaking primitive in distributed computing. Whereas degree-Δ graphs may require palettes of Δ+1 colors in the worst case, it is well known that the chromatic number of many natural graph classes can be much smaller. In this paper we give new distributed algorithms to find (Δ/k)-coloring in graphs of girth 4 (triangle-free graphs), girth 5, and trees, where k is at most $(\frac{1}{4}-o(1))\ln\Delta$ in triangle-free graphs and at most (1−o(1))ln Δ in girth-5 graphs and trees, and o(1) is a function of Δ. Specifically, for Δ sufficiently large we can find such a coloring in O(k+log*n) time. Moreover, for any Δ we can compute such colorings in roughly logarithmic time for triangle-free and girth-5 graphs, and in O(logΔ+logΔ logn) time on trees. As a byproduct, our algorithm shows that the chromatic number of triangle-free graphs is at most $(4+o(1))\frac{\Delta}{\ln\Delta}$, which improves on Jamall's recent bound of $(67+o(1))\frac{\Delta}{\ln\Delta}$. Also, we show that (Δ+1)-coloring for triangle-free graphs can be obtained in sublogarithmic time for any Δ.