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Completely Disconnecting the Complete Graph
SIAM Journal on Discrete Mathematics, 2000Let \(\omega \in {\mathbb{N}} \cup \{\infty\}\). By ``completely disconnecting a graph \(G\)'' the authors mean a sequence \(G= G_0, G_1, \ldots, G_t\) of spanning subgraphs of \(G\) where \(G_t\) has no edge and \(G_{i+1}\) is obtained from \(G_i\) by deleting at most \(\omega\) edges with no more than one edge being deleted from any connected ...
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Detachments of Complete Graphs
Combinatorics, Probability and Computing, 2005A detachment of a graph $G$ is formed by splitting each vertex into one or more subvertices, and sharing the incident edges arbitrarily among the subvertices. In this paper we consider the question of whether a graph $H$ is a detachment of some complete graph $K_n$.
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