Exploration of k-edge-deficient temporal graphs

Abstract A temporal graph with lifetime L is a sequence of graphs $$G_1, \ldots ,G_L$$ G 1 , … L , called layers, all which have the same vertex set V but can different edge sets. The underlying that contains edges appear in at least one layer. always connected if each layer graph, and it k -edge-deficient except most graph. For given start s exploration walk starts traverses layer, visits vertices We show always-connected, sufficient be explored $$O(kn \log n)$$ O ( k n log ) time steps. also construct for any requires $$\varOmega (n k)$$ Ω 1-edge-deficient graphs, we O ( n ) steps suffice exploration.