Graph r-hued colorings—A survey
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 …
neighbors of each vertex of degree d will receive at least min {d, r} different colors. The r …
[HTML][HTML] The square of a planar cubic graph is 7-colorable
The square of a planar cubic graph is 7-colorable - ScienceDirect Skip to main contentSkip to
article Elsevier logo Journals & Books Help Search My account Sign in View PDF Download …
article Elsevier logo Journals & Books Help Search My account Sign in View PDF Download …
[HTML][HTML] An introduction to the discharging method via graph coloring
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 …
is not to exhaustively survey results proved by this technique, but rather to demystify the …
Coloring, list coloring, and painting squares of graphs (and other related problems)
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) …
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …
List colouring squares of planar graphs
List Colouring Squares of Planar Graphs Page 1 List Colouring Squares of Planar Graphs
Frédéric Haveta,1, Jan van den Heuvelb,1, Colin McDiarmidc,1, and Bruce Reedd,1 a …
Frédéric Haveta,1, Jan van den Heuvelb,1, Colin McDiarmidc,1, and Bruce Reedd,1 a …
Proper conflict-free list-coloring, odd minors, subdivisions, and layered treewidth
Proper conflict-free coloring is an intermediate notion between proper coloring of a graph
and proper coloring of its square. It is a proper coloring such that for every non-isolated …
and proper coloring of its square. It is a proper coloring such that for every non-isolated …
Square coloring planar graphs with automatic discharging
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 …
problems. Its major downside is that it often requires lengthy case analyses, which are …
Every subcubic graph is packing -colorable
X Liu, X Zhang, Y Zhang - arxiv preprint arxiv:2404.09337, 2024 - arxiv.org
For a sequence $ S=(s_1,\ldots, s_k) $ of non-decreasing integers, a packing $ S $-coloring
of a graph $ G $ is a partition of its vertex set $ V (G) $ into $ V_1,\ldots, V_k $ such that for …
of a graph $ G $ is a partition of its vertex set $ V (G) $ into $ V_1,\ldots, V_k $ such that for …
2-Distance List -Coloring of Sparse Graphs
A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex
has a list of at least k available colors and vertices at distance at most 2 cannot share the …
has a list of at least k available colors and vertices at distance at most 2 cannot share the …
Partition subcubic planar graphs into independent sets
X Liu, Y Wang - arxiv preprint arxiv:2408.12189, 2024 - arxiv.org
A packing $(1^{\ell}, 2^ k) $-coloring of a graph $ G $ is a partition of $ V (G) $ into $\ell $
independent sets and $ k $ $2 $-independent sets (whose pairwise vertex distance is at …
independent sets and $ k $ $2 $-independent sets (whose pairwise vertex distance is at …