| Naslov: | A dichotomy for 1-planarity with restricted crossing types parameterized by treewidth |
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| Avtorji: | ID Cabello, Sergio (Avtor)
ID Dobler, Alexander (Avtor)
ID Fijavž, Gašper (Avtor)
ID Hamm, Thekla (Avtor)
ID Wagner, Mirko H. (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (843,13 KB)
MD5: 99F8A2DEAC75183A893C2DA5D3178B14
 URL - Izvorni URL, za dostop obiščite https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.16
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.08 - Objavljeni znanstveni prispevek na konferenci |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | A drawing of a graph is 1-planar if each edge participates in at most one crossing and adjacent edges do not cross. Up to symmetry, each crossing in a 1-planar drawing belongs to one out of six possible crossing types, where a type characterizes the subgraph induced by the four vertices of the crossing edges. Each of the 63 possible nonempty subsets ${\mathcal S}$ of crossing types gives a recognition problem: does a given graph admit an ${\mathcal S}$-restricted drawing, that is, a 1-planar drawing where the crossing type of each crossing is in ${\mathcal S}$? We show that there is a set ${\mathcal S}_{\rm bad}$ with three crossing types and the following properties: (i) If ${\mathcal S}$ contains no crossing type from ${\mathcal S}_{\rm bad}$, then the recognition of graphs that admit an ${\mathcal S}$-restricted drawing is fixed-parameter tractable with respect to the treewidth of the input graph. (ii) If ${\mathcal S}$ contains any crossing type from ${\mathcal S}_{\rm bad}$, then it is NP-hard to decide whether a graph has an ${\mathcal S}$-restricted drawing, even when considering graphs of constant pathwidth. We also extend this characterization of crossing types to 1-planar straight-line drawings and show the same complexity behaviour parameterized by treewidth. |
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| Ključne besede: | 1-planar, crossing type, treewidth, pathwidth |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Leto izida: | 2025 |
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| Št. strani: | 15 str. |
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| PID: | 20.500.12556/DiRROS-25062  |
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| UDK: | 004.42:519.17 |
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| DOI: | 10.4230/LIPIcs.ISAAC.2025.16 |
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| COBISS.SI-ID: | 263974915 |
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| Opomba: |
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| Datum objave v DiRROS: | 08.01.2026 |
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| Število ogledov: | 491 |
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| Število prenosov: | 247 |
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| Metapodatki: |    |
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