Graph coloring is a fundamental graph problem that is widely applied in a variety of
applications. The aim of graph coloring is to minimize the number of colors used to color the …

Structural graph parameters, such as treewidth, pathwidth, and clique-width, are a central
topic of study in parameterized complexity. A main aim of research in this area is to …

The first-fit coloring is a heuristic that assigns to each vertex, arriving in a specified order σ,
the smallest available color. The problem Grundy Coloring asks how many colors are …

One method to obtain a proper vertex coloring of graphs using a reasonable number of
colors is to start from any arbitrary proper coloring and then repeat some local re-coloring …

Following a given ordering of the edges of a graph G, the greedy edge colouring procedure
assigns to each edge the smallest available colour. The minimum number of colours thus …

Given a graph G=(V, E), a connected Grundy coloring is a proper vertex coloring that can be
obtained by a first-fit heuristic on a connected vertex sequence. A first-fit coloring heuristic is …

The classic greedy coloring (first-fit) algorithm considers the vertices of an input graph $ G $
in a given order and assigns the first available color to each vertex $ v $ in $ G $. In the {\sc …

A connected ordering (v 1, v 2,…, vn) of V (G) is an ordering of the vertices such that vi has at
least one neighbor in {v 1,…, vi− 1} for every i∈{2,…, n}. A connected greedy coloring (CGC …

Let G be a graph. We introduce the acyclic b-chromatic number of G as an analogue to the b-
chromatic number of G. An acyclic coloring of a graph G is a map c: V (G)→{1,…, k} such that …

A map $ c: V (G)\rightarrow\{1,\dots, k\} $ of a graph $ G $ is a packing $ k $-coloring if every
two different vertices of the same color $ i\in\{1,\dots, k\} $ are at distance more than $ i …