| Title: | Plane triangulations without large 2-trees |
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| Authors: | ID Bickle, Allan (Author)
ID Brinkmann, Gunnar (Author) |
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| Files: |  AMC_Bickle,Brinkmann_2026.pdf (339,53 KB)
MD5: 80DFDE7E53AEA80B212D5B82621809DF
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | In 1995 Leizhen Cai asked whether each plane triangulation has a spanning 2-tree. This question was recently answered in the negative by Bickle. He gave a plane triangulation on 38 vertices for which each 2-tree contained in it misses at least one vertex. We give a smaller example on 29 vertices and show that for each c>0 there are plane triangulations P=(V,E), so that each 2-tree that is a subgraph of P contains fewer than c|V| vertices. We also give a lower bound for the size of a maximum 2-tree in plane triangulations by proving that each plane triangulation P=(V,E) contains a 2-tree on at least log_2 (|V|-1)+4 -log_2 3 vertices. Finally we give structural criteria based on the decomposition trees of Jackson and Yu that guarantee the existence of spanning 2-trees in plane triangulations. The results are proven by using the close relation of 2-trees to hamiltonian cycles and to induced trees in the dual for plane triangulations without separating triangles. |
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| Keywords: | 2-tree, triangulation, Hamiltonian cycle, Yutsis partition |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 11.11.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 15 str. |
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| Numbering: | Vol. 26, no. 1, [article no.] P1.03 |
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| PID: | 20.500.12556/RUP-22287  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3066.5bf |
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| Publication date in RUP: | 21.12.2025 |
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| Views: | 223 |
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| Downloads: | 1 |
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