- Tytuł:
- All Tight Descriptions of 3-Stars in 3-Polytopes with Girth 5
- Autorzy:
-
Borodin, Oleg V.
Ivanova, Anna O. - Powiązania:
- https://bibliotekanauki.pl/articles/31342193.pdf
- Data publikacji:
- 2017-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
3-polytope
planar graph
structure properties
k -star - Opis:
- Lebesgue (1940) proved that every 3-polytope P5 of girth 5 has a path of three vertices of degree 3. Madaras (2004) refined this by showing that every P5 has a 3-vertex with two 3-neighbors and the third neighbor of degree at most 4. This description of 3-stars in P5s is tight in the sense that no its parameter can be strengthened due to the dodecahedron combined with the existence of a P5 in which every 3-vertex has a 4-neighbor. We give another tight description of 3-stars in P5s: there is a vertex of degree at most 4 having three 3-neighbors. Furthermore, we show that there are only these two tight descriptions of 3-stars in P5s. Also, we give a tight description of stars with at least three rays in P5s and pose a problem of describing all such descriptions. Finally, we prove a structural theorem about P5s that might be useful in further research.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 5-12
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł