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 …
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 …
Fractional list packing for layered graphs
S Cambie, WC van Batenburg - arXiv preprint arXiv:2410.02695, 2024 - arxiv.org
The fractional list packing number $\chi_ {\ell}^{\bullet}(G) $ of a graph $ G $ is a graph
invariant that has recently arisen from the study of disjoint list-colourings. It measures how …
invariant that has recently arisen from the study of disjoint list-colourings. It measures how …
Robust connectivity of graphs on surfaces
Let Λ(T) denote the set of leaves in a tree T. One natural problem is to look for a spanning
tree T of a given graph G such that Λ(T) is as large as possible. This problem is called …
tree T of a given graph G such that Λ(T) is as large as possible. This problem is called …
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 …
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 …
Turán problems in extremal graph theory and graph flexibility
KE Murphy - 2021 - search.proquest.com
In this work we will study two distinct areas of graph theory: generalized Turan problems and
graph flexibility. In the first chapter, we will provide some basic definitions and motivation …
graph flexibility. In the first chapter, we will provide some basic definitions and motivation …