After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

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 …

Let G be a graph with no isolated vertices. A k-coupon coloring of G is an assignment of
colors from [k]≔{1, 2,…, k} to the vertices of G such that the neighborhood of every vertex of …

A vertex coloring of a graph G=(V, E) that uses k colors is called an injective k-coloring of G if
no two vertices having a common neighbor have the same color. The minimum k for which G …

Let G be a graph without isolated vertices. A k-coupon coloring of G is ak-coloring of G such
that the neighborhood of every vertex of G contains vertices of all colors from k={1, 2, ..., k\} …

A vertex coloring is said to be 2-distance if any two distinct vertices of distance at most 2
receive different colors. Let G be a planar graph with girth at least 5. In this paper, we prove …

We study squares of planar graphs with the aim to determine their list chromatic number. We
present new upper bounds for the square of a planar graph with maximum degree …

Three edges e 1, e 2 and e 3 in a graph G are consecutive if they form a path (in this order)
or a cycle of length 3. The injective edge coloring number χ i′(G) is the minimum number of …

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

An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if
a path of length two exists between them. Let G be a plane graph with g (G)≥ 5 and χ i (G) …