## Abstract Let __G__=(__V, E__) be a graph where every vertex __v__∈__V__ is assigned a list of available colors __L__(__v__). We say that __G__ is list colorable for a given list assignment if we can color every vertex using its list such that adjacent vertices get different colors. If __L__(__v_
Vertex Partitions of K4,4-Minor Free Graphs
✍ Scribed by Leif K. Jørgensen
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 121 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0911-0119
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📜 SIMILAR VOLUMES
Let G be an infinite graph; define de& G to be the least m such that any partition P of the vertex set of G into sets of uniformly bounded cardinality contains a set which is adjacent to at least m Other sets of the partition. If G is either a regular tree 01 a triangtiisr, sqzart or hexagonal plana
## Abstract A __k‐tree__ is a chordal graph with no (__k__ + 2)‐clique. An ℓ‐__tree‐partition__ of a graph __G__ is a vertex partition of __G__ into ‘bags,’ such that contracting each bag to a single vertex gives an ℓ‐tree (after deleting loops and replacing parallel edges by a single edge). We pro
Thomassen, 1994 showed that all planar graphs are 5-choosable. In this paper we extend this result, by showing that all Ks-minor-free graphs are 5-choosable. (~) 1998 Elsevier Science B.V.
Given an infinite graph G, let deg,(G) be defined as the smallest d for which V(G) can be partitioned into finite subsets of (uniformly) bounded size such that each part is adjacent to at most d others. A countable graph G is constructed with de&(G) > 2 and with the property that [{y~V(G):d(x, y)sn}