### Abstract

Let G be a simple graph, L(v) a list of allowed colors assigned to each vertex v of G, and U an arbitrary subset of the vertex set. The graph G is called k-choosable if, for any list assignment with |L(v)| =k for all v ∈ V, it is possible to color all vertices with colors from their lists in a proper way (i.e., no monochromatic edge occurs). We say that G is U-reducible if, for every list assignment of G where all lists have the same number of elements, we can color the vertices of U with colors from their lists such that for every vertex v ∉ U at most one color of L(v) appears in the coloring of those neighbors of v which belong to U. The concept of reducibility is closely related to list colorings and choosability. The main result of this paper states that a bipartite graph G is U-reducible for every set U if and only if G is 2-choosable.

Original language | English |
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Pages (from-to) | 247-256 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 79 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Nov 27 1997 |

### Keywords

- Choosability
- Graph
- List coloring
- Vertex coloring

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*79*(1-3), 247-256. https://doi.org/10.1016/S0166-218X(97)00046-2