Recognition Complexity of Subgraphs of k-Connected Planar Cubic Graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910647214669824 |
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| author | Goetze, Miriam Jungeblut, Paul Ueckerdt, Torsten |
| author_facet | Goetze, Miriam Jungeblut, Paul Ueckerdt, Torsten |
| contents | We study the recognition complexity of subgraphs of k-connected planar cubic graphs for k = 1, 2, 3. We present polynomial-time algorithms to recognize subgraphs of 1- and 2-connected planar cubic graphs, both in the variable and fixed embedding setting. The main tools involve the Generalized (Anti)factor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case. Secondly, we prove NP-hardness of recognizing subgraphs of 3-connected planar cubic graphs in the variable embedding setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recognition Complexity of Subgraphs of k-Connected Planar Cubic Graphs Goetze, Miriam Jungeblut, Paul Ueckerdt, Torsten Discrete Mathematics Combinatorics We study the recognition complexity of subgraphs of k-connected planar cubic graphs for k = 1, 2, 3. We present polynomial-time algorithms to recognize subgraphs of 1- and 2-connected planar cubic graphs, both in the variable and fixed embedding setting. The main tools involve the Generalized (Anti)factor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case. Secondly, we prove NP-hardness of recognizing subgraphs of 3-connected planar cubic graphs in the variable embedding setting. |
| title | Recognition Complexity of Subgraphs of k-Connected Planar Cubic Graphs |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2401.05892 |