| Title: | 1-perfectly orientable K[sub]4-minor-free and outerplanar graphs |
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| Authors: | ID Brešar, Boštjan (Author)
ID Hartinger, Tatiana Romina (Author)
ID Kos, Tim (Author)
ID Milanič, Martin (Author) |
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| Files: |  https://doi.org/10.1016/j.dam.2017.09.017
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | A graph ▫$G$▫ is said to be 1-perfectly orientable if it has an orientation ▫$D$▫ such that for every vertex ▫$v \in V(G)$▫, the out-neighborhood of ▫$v$▫ in ▫$D$▫ is a clique in ▫$G$▫. D. J. Skrien [J. Graph Theory 6, 309--316 (1982)] posed the problem of characterizing the class of 1-perfectly orientable graphs. This graph class forms a common generalization of the classes of chordal and circular arc graphs; however, while polynomially recognizable via a reduction to 2-SAT, no structural characterization of this intriguing class of graphs is known. Based on a reduction of the study of 1-perfectly orientable graphs to the biconnected case, we characterize, both in terms of forbidden induced minors and in terms of composition theorems, the classes of 1-perfectly orientable ▫$K_4$▫-minor-free graphs and of 1-perfectly orientable outerplanar graphs. As part of our approach, we introduce a class of graphs defined similarly as the class of 2-trees and relate the classes of graphs under consideration to two other graph classes closed under induced minors studied in the literature: cyclically orientable graphs and graphs of separability at most 2. |
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| Keywords: | 1-perfectly orientable graph, ▫$K_4$▫-minor-free graph, outerplanar graph |
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| Year of publishing: | 2018 |
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| Number of pages: | 33-45 |
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| Numbering: | Vol. 248 |
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| PID: | 20.500.12556/DKUM-78962  |
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| UDC: | 519.17 |
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| ISSN on article: | 0166-218X |
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| COBISS.SI-ID: | 1540044740 |
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| DOI: | 10.1016/j.dam.2017.09.017 |
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| Publication date in DKUM: | 20.09.2022 |
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| Views: | 665 |
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| Downloads: | 18 |
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| Metadata: |    |
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| Categories: | Misc.
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