Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
Detachments Preserving Local Edge-Connectivity of Graphs
SIAM Journal on Discrete Mathematics
Detachment of Vertices of Graphs Preserving Edge-Connectivity
SIAM Journal on Discrete Mathematics
Highly edge-connected detachments of graphs and digraphs
Journal of Graph Theory
A detachment algorithm for inferring a graph from path frequency
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
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For a graph G, a detachment operation at a vertex transforms the graph into a new graph by splitting the vertex into several vertices in such a way that the original graph can be obtained by contracting all the split vertices into a single vertex. A graph obtained from a given graph G by applying detachment operations at several vertices is called a detachment of graph G. While detachment operations may decrease the connectivity of graphs, there are several works on conditions for preserving the connectivity. In this paper, we present necessary and sufficient conditions for a given graph/digraph to have an Eulerian detachment that satisfies a given local edge-connectivity requirement. We also discuss conditions for the detachment to be loopless.