Highly edge-connected detachments of graphs and digraphs
نویسندگان
چکیده
Let G = (V, E) be a graph or digraph and r : V → Z+. An r-detachment of G is a graph H obtained by ‘splitting’ each vertex v ∈ V into r(v) vertices. The vertices v1, ..., vr(v) obtained by splitting v are called the pieces of v in H. Every edge uv ∈ E corresponds to an edge of H connecting some piece of u to some piece of v. Crispin Nash-Williams [9] gave necessary and sufficient conditions for a graph to have a k-edge-connected r-detachment. He also solved the version where the degrees of all the pieces are specified. In this paper we solve the same problems for directed graphs. We also give a simple and self-contained new proof for the undirected result.
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عنوان ژورنال:
- Journal of Graph Theory
دوره 43 شماره
صفحات -
تاریخ انتشار 2003