On the Weight of Minor Faces in Triangle-Free 3-Polytopes
The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sh...
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Sciendo
2016-08-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1877 |
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doaj-0f54f7375ca14b5ab726e5a8b6a4a9a62021-09-05T17:20:21ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922016-08-0136360361910.7151/dmgt.1877dmgt.1877On the Weight of Minor Faces in Triangle-Free 3-PolytopesBorodin Oleg V.0Ivanova Anna O.1Institute of Mathematics Siberian Branch Russian Academy of Sciences, Novosibirsk, 630090, RussiaAmmosov North-Eastern Federal University Yakutsk, 677000, RussiaThe weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sharp, but it was still unknown whether 21 is sharp.https://doi.org/10.7151/dmgt.1877plane mapplane graph3-polytopestructural propertyweight of face |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Borodin Oleg V. Ivanova Anna O. |
| spellingShingle |
Borodin Oleg V. Ivanova Anna O. On the Weight of Minor Faces in Triangle-Free 3-Polytopes Discussiones Mathematicae Graph Theory plane map plane graph 3-polytope structural property weight of face |
| author_facet |
Borodin Oleg V. Ivanova Anna O. |
| author_sort |
Borodin Oleg V. |
| title |
On the Weight of Minor Faces in Triangle-Free 3-Polytopes |
| title_short |
On the Weight of Minor Faces in Triangle-Free 3-Polytopes |
| title_full |
On the Weight of Minor Faces in Triangle-Free 3-Polytopes |
| title_fullStr |
On the Weight of Minor Faces in Triangle-Free 3-Polytopes |
| title_full_unstemmed |
On the Weight of Minor Faces in Triangle-Free 3-Polytopes |
| title_sort |
on the weight of minor faces in triangle-free 3-polytopes |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2016-08-01 |
| description |
The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sharp, but it was still unknown whether 21 is sharp. |
| topic |
plane map plane graph 3-polytope structural property weight of face |
| url |
https://doi.org/10.7151/dmgt.1877 |
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AT borodinolegv ontheweightofminorfacesintrianglefree3polytopes AT ivanovaannao ontheweightofminorfacesintrianglefree3polytopes |
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1717786475616010240 |