Abstract A (k, r)-coloring of a graph G is a proper k-vertex coloring of G such that the
neighbors of each vertex of degree d will receive at least min {d, r} different colors. The r …

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 …

arXiv:2210.05915v2 [math.CO] 22 Apr 2023 Page 1 arXiv:2210.05915v2 [math.CO] 22 Apr
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …

arXiv:1604.06504v1 [math.CO] 21 Apr 2016 Page 1 arXiv:1604.06504v1 [math.CO] 21 Apr
2016 The chromatic number of the square of subcubic planar graphs Stephen G. Hartke∗ …

The discharging method is a powerful proof technique, especially for graph coloring
problems. Its major downside is that it often requires lengthy case analyses, which are …

The square G 2 of a graph G is the graph on the same vertex set as G in which two vertices
u, v are adjacent if and only if uv∈ E (G), or u and v have at least one common neighbor in …

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 …

Using computational techniques we provide a framework for proving results on subclasses
of planar graphs via discharging method. The aim of this paper is to apply these techniques …

A $2 $-distance $ k $-coloring of a graph is a proper vertex $ k $-coloring where vertices at
distance at most 2 cannot share the same color. We prove the existence of a $2 $-distance …

Given a graph G and a list assignment L (v) for each vertex of v of G, a proper L-list-coloring
of G is a function that maps every vertex to a color in L (v) such that no pair of adjacent …