On the path separation number of graphs
Abstract
A path separator of a graph G is a set of paths P=\P1,…,Pt\ such that for every pair of edges e,f∈ E(G), there exist paths Pe,Pf∈P such that e∈ E(Pe), f∈ E(Pe), e∈ E(Pf) and f∈ E(Pf). The path separation number of G, denoted psn(G), is the smallest number of paths in a path separator. We shall estimate the path separation number of several graph families, including complete graphs, random graph, the hypercube, and discuss general graphs as well.
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