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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.19270 |
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| _version_ | 1866911592345501696 |
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| author | Aboulker, Pierre Oijid, Nacim Petit, Robin Rocton, Mathis Simon, Christopher-Lloyd |
| author_facet | Aboulker, Pierre Oijid, Nacim Petit, Robin Rocton, Mathis Simon, Christopher-Lloyd |
| contents | Given a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The degreewidth of a digraph is the minimum over all ordering of the maximum degree of the backedge graph. We answer an open question by Keeney and Lokshtanov [WG 2024], proving that it is \NP-hard to determine whether an oriented graph has degreewidth at most $1$, which settles the last open case for oriented graphs. We complement this result with a general discussion on parameters defined using backedge graphs and their relations to classical parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19270 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing the degreewidth of a digraph is hard Aboulker, Pierre Oijid, Nacim Petit, Robin Rocton, Mathis Simon, Christopher-Lloyd Combinatorics Given a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The degreewidth of a digraph is the minimum over all ordering of the maximum degree of the backedge graph. We answer an open question by Keeney and Lokshtanov [WG 2024], proving that it is \NP-hard to determine whether an oriented graph has degreewidth at most $1$, which settles the last open case for oriented graphs. We complement this result with a general discussion on parameters defined using backedge graphs and their relations to classical parameters. |
| title | Computing the degreewidth of a digraph is hard |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.19270 |