Directed request graphs need n - cc + dfvs temporal arcs; undirected strongly connected requests allow n-1 edges iff every collection of pairwise non-vertex-disjoint closed walks shares a vertex, testable in polynomial time.
Akrida, Leszek Gasieniec, George B
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Designing sparse temporal graphs satisfying connectivity requirements
Directed request graphs need n - cc + dfvs temporal arcs; undirected strongly connected requests allow n-1 edges iff every collection of pairwise non-vertex-disjoint closed walks shares a vertex, testable in polynomial time.