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Vertex colouring edge partitions. (English) Zbl 1074.05031
Suppose that the edges of a graph are assigned labels from a $$k$$-set, or equivilently, the edges are partitioned into $$k$$ parts. Each vertex $$v$$ has an associated multiset $$X_v$$ consisting of the labels on its incident edges. The partition is a (proper) vertex coloring if for every edge $$uv$$, $$X_u \neq X_v$$.
The authors show that the edges of any graph (except those containing a component isomorphic to $$K_2$$) have a partition into four parts such that the associated multisets form a vertex coloring. Moreover, if the minimum degree is at least 1000, then the edges can be partitioned into three parts yielding a vertex coloring.
This paper is well written and the result is interesting.

MSC:
 05C15 Coloring of graphs and hypergraphs
Full Text:
References:
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