A graph is k-degenerate if every subgraph H has a vertex v with d H (v)≤ k. The class of
degenerate graphs plays an important role in the graph coloring theory. Observed that every …

Weak degeneracy is a variation of degeneracy which shares many nice properties of
degeneracy. In particular, if a graph $ G $ is weakly $ d $-degenerate, then for any $(d+ 1) …

This paper introduces the concept of weak $^* $ degeneracy of a graph that shares many
nice properties of degeneracy. We prove that for any $ f: V (G)\to\mathbb {N} $, if $ G $ is …

Motivated by the study of greedy algorithms for graph coloring, Bernshteyn and Lee
introduced a generalization of graph degeneracy, which is called weak degeneracy. In this …

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 …

图的弱退化度是由Bernshteyn 和Lee 提出的一个新定义, 是图的退化度的变形. 根据定义可知,
每个d-退化的图也是d-弱退化的. 另一方面, 如果G 是弱退化的, 那么χ (G)≤ χl (G)≤ χDP (G)≤ …

Bernshteyn and Lee defined a new notion, weak degeneracy, which is slightly weaker than
the ordinary degeneracy. It is proved that strictly $ f $-degenerate transversal is a common …

Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to
many graph coloring parameters. In this article, we prove that planar graphs with distance of …

Abstract A graph is (I, F)-partitionable if its vertex set can be partitioned into two parts such
that one part I is an independent set, and the other F induces a forest. A graph is k …

Defective coloring (also known as relaxed or improper coloring) is a generalization of proper
coloring defined as follows: for $ d\in\mathbb {N} $, a coloring of a graph is $ d $-defective if …