Disjoint list-colorings for planar graphs
One of Thomassen's classical results is that every planar graph of girth at least $5 $ is 3-
choosable. One can wonder if for a planar graph $ G $ of girth sufficiently large and a $3 …
choosable. One can wonder if for a planar graph $ G $ of girth sufficiently large and a $3 …
Flexible list colorings: Maximizing the number of requests satisfied
Flexible list coloring was introduced by Dvořák, Norin, and Postle in 2019. Suppose 0≤ ϵ≤
1 0≤ϵ≤1, GG is a graph, LL is a list assignment for GG, and rr is a function with nonempty …
1 0≤ϵ≤1, GG is a graph, LL is a list assignment for GG, and rr is a function with nonempty …
Flexible list colorings in graphs with special degeneracy conditions
For a given ε> 0 ε\gt0, we say that a graph GG is ε ε‐flexibly kk‐choosable if the following
holds: for any assignment LL of color lists of size kk on V (G) V(G), if a preferred color from a …
holds: for any assignment LL of color lists of size kk on V (G) V(G), if a preferred color from a …
[HTML][HTML] Flexibility of planar graphs—sharpening the tools to get lists of size four
A graph where each vertex v has a list L (v) of available colors is L-colorable if there is a
proper coloring such that the color of v is in L (v) for each v. A graph is k-choosable if every …
proper coloring such that the color of v is in L (v) for each v. A graph is k-choosable if every …
Flexibility of graphs with maximum average degree less than
R Bi, P Bradshaw - arXiv preprint arXiv:2310.02979, 2023 - arxiv.org
In the flexible list coloring problem, we receive a graph $ G $ and a color list assignment $ L
$ on $ G $, as well as a set of coloring preferences at some vertex subset of $ G $, as input …
$ on $ G $, as well as a set of coloring preferences at some vertex subset of $ G $, as input …
Flexibility of planar graphs without 4-cycles
T Masařík - arXiv preprint arXiv:1903.01460, 2019 - arxiv.org
Proper graph coloring assigns different colors to adjacent vertices of the graph. Usually, the
number of colors is fixed or as small as possible. Consider applications (eg variants of …
number of colors is fixed or as small as possible. Consider applications (eg variants of …
Flexibility of planar graphs without and
D Yang, F Yang - arXiv preprint arXiv:2006.05243, 2020 - arxiv.org
Let $ G $ be a $\{C_4, C_5\} $-free planar graph with a list assignment $ L $. Suppose a
preferred color is given for some of the vertices. We prove that if all lists have size at least …
preferred color is given for some of the vertices. We prove that if all lists have size at least …
Graphs of maximum average degree less than are flexibly -choosable
R Bi, P Bradshaw - arXiv preprint arXiv:2408.08393, 2024 - arxiv.org
We consider the flexible list coloring problem, in which we have a graph $ G $, a color list
assignment $ L: V (G)\rightarrow 2^{\mathbb N} $, and a set $ U\subseteq V (G) $ of vertices …
assignment $ L: V (G)\rightarrow 2^{\mathbb N} $, and a set $ U\subseteq V (G) $ of vertices …
[HTML][HTML] On weak flexibility in planar graphs
Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on
graphs (J Graph Theory 92 (3): 191–206, 2019, https://doi. org/10.1002/jgt. 22447). In this …
graphs (J Graph Theory 92 (3): 191–206, 2019, https://doi. org/10.1002/jgt. 22447). In this …
On sufficient conditions for planar graphs to be 5-flexible
F Yang - Graphs and Combinatorics, 2022 - Springer
In this paper, we study the flexibility of two planar graph classes H 1, H 2, where H 1, H 2
denote the set of all hopper-free planar graphs and house-free planar graphs, respectively …
denote the set of all hopper-free planar graphs and house-free planar graphs, respectively …