A conflict-free coloring of a graph with respect to open (resp., closed) neighborhood is a
coloring of vertices such that for every vertex there is a color appearing exactly once in its …

A vertex coloring of a graph is said to be conflict-free with respect to neighborhoods if for
every non-isolated vertex there is a color appearing exactly once in its (open) neighborhood …

An odd c-coloring of a graph is a proper c-coloring such that each non-isolated vertex has a
color appearing an odd number of times on its neighborhood. This concept was introduced …

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears
an odd number of times on its neighborhood. This notion was recently introduced by …

An odd coloring of a graph G is a proper coloring such that any non-isolated vertex in G has
a color appearing an odd number of times on its neighbors. The odd chromatic number …

Given a graph $ G $, a vertex-colouring $\sigma $ of $ G $, and a subset $ X\subseteq V (G)
$, a colour $ x\in\sigma (X) $ is said to be\emph {odd} for $ X $ in $\sigma $ if it has an odd …

A proper vertex colouring of a graph G is conflict-free if in the neighbourhood of every vertex
some colour appears exactly once, while it is called h-conflict-free if there are at least h such …

The following relaxation of proper coloring the square of a graph was recently introduced: for
a positive integer h, the proper h-conflict-free chromatic number of a graph G, denoted χ pcf …

An odd c-coloring of a graph is a proper c-coloring such that each non-isolated vertex has a
color appearing an odd number of times within its open neighborhood. A proper conflict-free …

A proper coloring of a graph is\emph {proper conflict-free} if every non-isolated vertex $ v $
has a neighbor whose color is unique in the neighborhood of $ v $. A proper coloring of a …