
Every toroidal graph without triangles adjacent to 5cycles is DP4colorable
DPcoloring, also known as correspondence coloring, is introduced by Dvo...
read it

DP4coloring of planar graphs with some restrictions on cycles
DPcoloring was introduced by Dvořák and Postle as a generalization of l...
read it

On the Chromatic Polynomial and Counting DPColorings
The chromatic polynomial of a graph G, denoted P(G,m), is equal to the n...
read it

Acyclic edge coloring conjecture is true on planar graphs without intersecting triangles
An acyclic edge coloring of a graph G is a proper edge coloring such tha...
read it

Flexibility of planar graphs without 4cycles
Proper graph coloring assigns different colors to adjacent vertices of t...
read it

Flexibility of planar graphs of girth at least six
Let G be a planar graph with a list assignment L. Suppose a preferred co...
read it

Classification of minimally unsatisfiable 2CNFs
We consider minimally unsatisfiable 2CNFs, i.e., minimally unsatisfiabl...
read it
3choosable planar graphs with some precolored vertices and no 5^cycles normally adjacent to 8^cycles
DPcoloring was introduced by Dvořák and Postle [J. Combin. Theory Ser. B 129 (2018) 38–54] as a generalization of list coloring. They used a "weak" version of DPcoloring to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of length 4 to 8 is 3choosable. Liu and Li improved the result by showing that every planar graph without adjacent cycles of length at most 8 is 3choosable. In this paper, it is showed that every planar graph without 5^cycles normally adjacent to 8^cycles is 3choosable. Actually, all these three papers give more stronger results by stating them in the form of "weakly" DP3coloring and color extension.
READ FULL TEXT
Comments
There are no comments yet.