# On Generalized Choice and Coloring Numbers

@article{Dvok2019OnGC, title={On Generalized Choice and Coloring Numbers}, author={Zdeněk Dvoř{\'a}k and Jakub Pek{\'a}rek and Jean-S{\'e}bastien Sereni}, journal={Electron. J. Comb.}, year={2019}, volume={26}, pages={1} }

A well-known result of Alon shows that the coloring number of a graph is bounded by a function of its choosability. We explore this relationship in a more general setting with relaxed assumptions on color classes, encoded by a graph parameter.

## 2 Citations

Generalized List Colouring of Graphs

- MathematicsGraphs Comb.
- 2021

This paper disproves a conjecture of Wang, Wu, Yan and Xie, and answers in negative a question in Dvorak, Pekarek and Sereni. In return, we pose five open problems.

Islands in minor-closed classes. I. Bounded treewidth and separators

- Mathematics
- 2017

The clustered chromatic number of a graph class is the minimum integer $t$ such that for some $C$ the vertices of every graph in the class can be colored in $t$ colors so that every monochromatic…

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