Abstract The Erdős--Faber--Lovász conjecture (posed in 1972) states that the chromatic
index of any linear hypergraph on n vertices is at most n. In this paper, we prove this …

arxiv:2210.05915v2 [math.CO] 22 Apr 2023 Page 1 arxiv:2210.05915v2 [math.CO] 22 Apr
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …

This paper provides a survey of methods, results, and open problems on graph and
hypergraph colourings, with a particular emphasis on semi-random “nibble” methods. We …

A PROOF OF THE ERDOS–FABER–LOVASZ CONJECTURE 1. Introduction Graph and
hypergraph colouring problems are central to comb Page 1 A PROOF OF THE ERDOS–FABER–LOVASZ …

An independent set may not contain both a vertex and one of its neighbours. This basic fact
makes the uniform distribution over independent sets rather special. We consider the hard …

Proper conflict-free coloring is an intermediate notion between proper coloring of a graph
and proper coloring of its square. It is a proper coloring such that for every non-isolated …

A proper edge coloring of a graph is strong if it creates no bichromatic path of length three. It
is well known that for a strong edge coloring of ak k‐regular graph at least 2 k− 1 2k-1 colors …

Given a graph $ G $, an injective edge-coloring of $ G $ is a function $\psi: E
(G)\rightarrow\mathbb N $ such that if $\psi (e)=\psi (e') $, then no third edge joins an …

In a proper edge‐coloring the edges of every color form a matching. A matching is induced if
the end‐vertices of its edges induce a matching. A strong edge‐coloring is an edge‐coloring …

An induced matching in a graph $ G $ is a matching such that its end vertices also induce a
matching. A $(1^{\ell}, 2^ k) $-packing edge-coloring of a graph $ G $ is a partition of its …