Independence free graphs and vertex connectivity augmentation
Journal of Combinatorial Theory Series B
Enumeration of the degree sequences of non-separable graphs and connected graphs
European Journal of Combinatorics
A detachment algorithm for inferring a graph from path frequency
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Multiply balanced edge colorings of multigraphs
Journal of Graph Theory
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Let G = (V, E) be a graph and r : V → Z+. An r-detachment of G is a graph H obtained by 'splitting' each vertex v ∈ V into r(v) vertices, 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. An r-degree specification for G is a function f on V, such that, for each vertex v ∈ V, f(v) is a partition of d(v) into r(v) positive integers. An f-detachment of G is an r-detachment H in which the degrees in H of the pieces of each v ∈ V are given by f(v). Crispin Nash-Williams [3] obtained necessary and sufficient conditions for a graph to have a k-edge-connected r-detachment or f-detachment. We solve a problem posed by Nash-Williams in [2] by obtaining analogous results for non-separable detachments of graphs.