Symmetry-breaking problems are among the most well studied in the field of distributed
computing and yet the most fundamental questions about their complexity remain open. In …

Over the past 30 years numerous algorithms have been designed for symmetry breaking
problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge …

The celebrated time hierarchy theorem for Turing machines states, informally, that more
problems can be solved given more time. The extent to which a time hierarchy--type theorem …

We prove that every triangle-free graph with maximum degree Δ has list chromatic number
at most (1+ o (1)) Δ ln⁡ Δ. This matches the best-known upper bound for graphs of girth at …

The (∆+ 1)-coloring problem is a fundamental symmetry breaking problem in distributed
computing. We give a new randomized coloring algorithm for (∆+ 1)-coloring running in O …

The aim of this note is twofold. On the one hand, we present a streamlined version of
Molloy's new proof of the bound for triangle‐free graphs G, avoiding the technicalities of the …

The Lovász Local Lemma is a classic result in probability theory that is often used to prove
the existence of combinatorial objects via the probabilistic method. In its simplest form, it …

Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle
finding) as well as triangle enumeration (triangle listing) play central roles in the field of …

We present the first super-linear lower bounds for natural graph problems in the CONGEST
model, answering a long-standing open question. Specifically, we show that any exact …

A recent palette sparsification theorem of Assadi, Chen, and Khanna [SODA'19] states that in
every $ n $-vertex graph $ G $ with maximum degree $\Delta $, sampling $ O (\log {n}) …