Finding nonseparating induced cycles and independent spanning trees in 3-connected graphs
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2019, Journal of Parallel and Distributed ComputingSimple computation of st-edge- and st-numberings from ear decompositions
2019, Information Processing LettersCitation Excerpt :Then there is an open ear decomposition that naturally depends on T (see e.g. [12]), and most of the algorithms above compute only st-numberings that are consistent with this special open ear decomposition. However, several applications (e.g. the ones in [2,5,13,11]) need more general st-numberings that are consistent with an arbitrary given open ear decomposition D. The following is a very simple and probably folklore approach to obtain these st-numberings by falling back on st-orientations (see e.g. [9, Section 3.1] and [13, Application 1]): Compute an open ear decomposition D, orient the first cycle from s to t, and orient every following ear such that acyclicity is preserved; since the reachability relation is always a poset, an appropriate orientation for the next ear is guaranteed to exist.