Given a digraph D=(V, A) on n vertices and a vertex v∈ V, the cycle-degree of v is the
minimum size of a set S⊆ V (D)∖{v} intersecting every directed cycle of D containing v. From …

The reconfiguration graph C k (G) for the k-colourings of a graph G has a vertex for each
proper k-colouring of G, and two vertices of C k (G) are adjacent precisely when those k …

Recoloring a graph is about finding a sequence of proper colorings of this graph from an
initial coloring $\sigma $ to a target coloring $\eta $. Adding the constraint that each pair of …

For any positive integer $ k $, the reconfiguration graph for all $ k $-colorings of a graph $ G
$, denoted by $\mathcal {R} _k (G) $, is the graph where vertices represent the $ k …

Fix a graph G, a list-assignment L for G, and L-colorings α and β. An L-recoloring sequence,
starting from α, recolors a single vertex at each step, so that each resulting intermediate …

The coloring reconfiguration graph C k (G) C_k(G) has as its vertex set all the proper kk‐
colorings of GG, and two vertices in C k (G) C_k(G) are adjacent if their corresponding kk …

A list assignment $ L $ of a graph $ G $ is a function that assigns to every vertex $ v $ of $ G
$ a set $ L (v) $ of colors. A proper coloring $\alpha $ of $ G $ is called an $ L $-coloring of …

This thesis focuses on a notion of colouring of digraphs introduced by ErdH {o} s and
Neumann-Lara in the late 1970s, namely the dicolouring, and its associated digraph …

Reconfiguration is the concept of moving between different solutions to a problem by
transforming one solution into another using some prescribed transformation rule (move) …

This thesis focuses on a notion of colouring of digraphs introduced by Erdos and Neumann-
Lara in the late 1970s, namely the dicolouring, and its associated digraph parameter: the …