The smallest integer k needed for the assignment of k colors to the elements so that the
coloring is proper (vertices and edges) is called the total chromatic number of a graph …

Consider the following two ways to colour the vertices of a graph where the requirement that
adjacent vertices get distinct colours is relaxed. A colouring has" defect" $ d $ if each …

We introduce a new variant of graph coloring called correspondence coloring which
generalizes list coloring and allows for reductions previously only possible for ordinary …

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 …

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It is well known that every planar graph contains a vertex of degree at most 5. A theorem of
Kotzig states that every 3-connected planar graph contains an edge whose endvertices …

While solving a question on the list coloring of planar graphs, Dvořák and Postle introduced
the new notion of DP-coloring (they called it correspondence coloring). A DP-coloring of a …

Alon (2000) proved that for any graph G, χ ℓ (G)= Ω (ln d), where χ ℓ (G) is the list chromatic
number of G and d is the average degree of G. Dvořák and Postle (2015) recently introduced …

We provide a “how-to” guide to the use and application of the Discharging Method. Our aim
is not to exhaustively survey results proved by this technique, but rather to demystify the …

DP-coloring (also known as correspondence coloring) is a generalization of list coloring
introduced recently by Dvořák and Postle [12]. Many known upper bounds for the list …