The key insights and highlights of the content are:
The author introduces the problem of computing the "edge-resilient strongly orientable blocks" of a mixed graph G. These are the maximal sets of vertices C1, C2, ..., Ck such that for every i and every edge e of G (directed or undirected), there is an orientation of G \ e where all vertices in Ci are strongly connected.
The author shows that this problem can be reduced to the computation of the 2-edge twinless strongly connected components (2eTSCCs) of a directed graph.
The author presents a linear-time algorithm for computing the 2eTSCCs by constructing a collection of auxiliary graphs that preserve the 2eTSCCs and have a simple structure after the deletion of any edge.
The algorithm works by first splitting the directed edges and replacing the undirected edges with a special gadget in the input mixed graph G. It then computes the 2eTSCCs of the resulting directed graph, and returns the sets of ordinary vertices in these components as the edge-resilient strongly orientable blocks of G.
As a consequence of the algorithm, the author shows that the edge-resilient strongly orientable blocks form a partition of the vertex set of the input mixed graph G.
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by Loukas Georg... at arxiv.org 04-15-2024
https://arxiv.org/pdf/2302.02215.pdfDeeper Inquiries