# Acyclic Choosability of Graphs with Small Maximum Degree

@inproceedings{Gonalves2005AcyclicCO, title={Acyclic Choosability of Graphs with Small Maximum Degree}, author={Daniel Gonçalves and Micka{\"e}l Montassier}, booktitle={WG}, year={2005} }

A proper vertex coloring of a graph G = (V,E) is acyclic if G contains no bicolored cycle. A graph G is L-list colorable if for a given list assignment L = {L(v) : v ∈ V}, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V. If G is L-list colorable for every list assignment with |L(v)| ≥ k for all v ∈ V, then G is said k-choosable. A graph is said to be acyclically k-choosable if the coloring obtained is acyclic. In this paper, we study the acyclic choosability of graphs…

## 6 Citations

RR-1423-07 Acyclic t-improper colourings of graphs with bounded maximum degree

- Mathematics
- 2007

For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour classes is acyclic and…

A conjecture of Borodin and a coloring of Grünbaum

- MathematicsJ. Graph Theory
- 2006

It is proved that every planar graph has a 5-coloring such that the union of every k color classes with 1 ⩽ k⩽ 4 induces a k-degenerate graph.

Acyclic Choosability of Graphs with Bounded Degree

- MathematicsActa Mathematica Sinica, English Series
- 2022

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