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 …

Abstract Montassier et al.(2006) asked to find the smallest positive integers d 0 and d 1 such
that planar graphs without {4, 5}-cycles and d Δ≥ d 0 are 3-choosable and planar graphs …

DP-coloring is a generalization of list-coloring, which was introduced by Dvořák and Postle.
Zhang showed that every planar graph with neither adjacent triangles nor 5-, 6-, 9-cycles is …

DP-coloring of graphs as a generalization of list coloring was introduced by Dvořák and
Postle (2018). In this paper, we show that every planar graph without intersecting 5-cycles is …

A graph G is k-degenerate if each subgraph of G has a vertex of degree at most k. It is known
that every simple planar graph with girth 6, or equivalently without 3-, 4-, and 5-cycles, is 2 …

DP-coloring was introduced by Dvořák and Postle as a generalization of list coloring. It was
originally used to solve a longstanding conjecture by Borodin, stating that every planar …

A graph G is k-degenerate if every subgraph of G has a vertex of degree at most k. It is
known that every planar graph of girth 6 (equivalently, without 3-, 4-, and 5-cycles) is 2 …

A weak DP-coloring is a new coloring combining DP-coloring and vertex-partition, which
was introduced by Sittitrai and Nakprasit. Sribunhung et al. proved that planar graphs …

DP-coloring of a graph was introduced by Dvorák and Postle [J. Combin. Theory Ser. B 129
(2018), 38–54] as a generalization of a list coloring. Kim and Ozeki [Discrete Math. 341 …

Let G be a graph and let f_i, i ∈ {1, ..., s\}, fi, i∈ 1,…, s, be a function from V (G) to the set of
nonnegative integers. In Sittitrai and Nakprasit (Analogue of DP-coloring on variable …