Informacja

Drogi użytkowniku, aplikacja do prawidłowego działania wymaga obsługi JavaScript. Proszę włącz obsługę JavaScript w Twojej przeglądarce.

English (EN)·Polski (PL)·Yкраїнський (UK)
Przejdź do strony domowej biblioteki Centralna Biblioteka Wojskowa Link otwiera się w nowym oknie Logo biblioteki Prolib Integro - strona głównaCentralna Biblioteka Wojskowa

Wyszukujesz frazę "Ivanova, A. V." wg kryterium: Autor

  Lista filtrów
Wyrównaj
    Wyświetlanie 1-4 z 4
    Tytuł:
    An Extension of Kotzig’s Theorem
    Autorzy:
    Aksenov, Valerii A.
    Borodin, Oleg V.
    Ivanova, Anna O.
    Powiązania:
    https://bibliotekanauki.pl/articles/31340608.pdf
    Data publikacji:
    2016-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    plane graph
    normal plane map
    structural property
    weight
    Opis:
    In 1955, Kotzig proved that every 3-connected planar graph has an edge with the degree sum of its end vertices at most 13, which is tight. An edge uv is of type (i, j) if d(u) ≤ i and d(v) ≤ j. Borodin (1991) proved that every normal plane map contains an edge of one of the types (3, 10), (4, 7), or (5, 6), which is tight. Cole, Kowalik, and Škrekovski (2007) deduced from this result by Borodin that Kotzig’s bound of 13 is valid for all planar graphs with minimum degree δ at least 2 in which every d-vertex, d ≥ 12, has at most d − 11 neighbors of degree 2. We give a common extension of the three above results by proving for any integer t ≥ 1 that every plane graph with δ ≥ 2 and no d-vertex, d ≥ 11+t, having more than d − 11 neighbors of degree 2 has an edge of one of the following types: (2, 10+t), (3, 10), (4, 7), or (5, 6), where all parameters are tight.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 4; 889-897
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    More About the Height of Faces in 3-Polytopes
    Autorzy:
    Borodin, Oleg V.
    Bykov, Mikhail A.
    Ivanova, Anna O.
    Powiązania:
    https://bibliotekanauki.pl/articles/31342325.pdf
    Data publikacji:
    2018-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    plane map
    planar graph
    3-polytope
    structural properties
    height of face
    Opis:
    The height of a face in a 3-polytope is the maximum degree of its incident vertices, and the height of a 3-polytope, h, is the minimum height of its faces. A face is pyramidal if it is either a 4-face incident with three 3-vertices, or a 3-face incident with two vertices of degree at most 4. If pyramidal faces are allowed, then h can be arbitrarily large, so we assume the absence of pyramidal faces in what follows. In 1940, Lebesgue proved that every quadrangulated 3-polytope has h ≤ 11. In 1995, this bound was lowered by Avgustinovich and Borodin to 10. Recently, Borodin and Ivanova improved it to the sharp bound 8. For plane triangulation without 4-vertices, Borodin (1992), confirming the Kotzig conjecture of 1979, proved that h ≤ 20, which bound is sharp. Later, Borodin (1998) proved that h ≤ 20 for all triangulated 3-polytopes. In 1996, Horňák and Jendrol’ proved for arbitrarily polytopes that h ≤ 23. Recently, Borodin and Ivanova obtained the sharp bounds 10 for trianglefree polytopes and 20 for arbitrary polytopes. In this paper we prove that any polytope has a face of degree at most 10 with height at most 20, where 10 and 20 are sharp.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 2; 443-453
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Low 5-Stars at 5-Vertices in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree from 7 to 9
    Autorzy:
    Borodin, Oleg V.
    Bykov, Mikhail A.
    Ivanova, Anna O.
    Powiązania:
    https://bibliotekanauki.pl/articles/31348144.pdf
    Data publikacji:
    2020-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    planar map
    planar graph
    3-polytope
    structural properties
    5-star
    weight
    height
    Opis:
    In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class $P_5$ of 3-polytopes with minimum degree 5. Given a 3-polytope $P$, by $h_5(P)$ we denote the minimum of the maximum degrees (height) of the neighborhoods of 5-vertices (minor 5-stars) in $P$. Recently, Borodin, Ivanova and Jensen showed that if a polytope $P$ in $P_5$ is allowed to have a 5-vertex adjacent to two 5-vertices and two more vertices of degree at most 6, called a (5, 5, 6, 6, ∞)-vertex, then $h_5(P)$ can be arbitrarily large. Therefore, we consider the subclass \(P_5^\ast\) of 3-polytopes in $P_5$ that avoid (5, 5, 6, 6, ∞)-vertices. For each $P^\ast$ in $P_5^\ast$ without vertices of degree from 7 to 9, it follows from Lebesgue’s Theorem that $h_5(P^\ast) ≤ 17$. Recently, this bound was lowered by Borodin, Ivanova, and Kazak to the sharp bound $h_5(P^\ast) ≤ 15$ assuming the absence of vertices of degree from 7 to 11 in $P^\ast$. In this note, we extend the bound $h_5(P^\ast) ≤ 15$ to all $P^\ast$s without vertices of degree from 7 to 9.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1025-1033
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Describing Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree 6 or 7
    Autorzy:
    Batueva, Ts.Ch-D.
    Borodin, O.V.
    Ivanova, A.O.
    Nikiforov, D.V.
    Powiązania:
    https://bibliotekanauki.pl/articles/32361718.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    planar graph
    structural properties
    3-polytope
    5-star
    neighborhood
    Opis:
    In 1940, in attempts to solve the Four Color Problem, Henry Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P5 of 3-polytopes with minimum degree 5. This description depends on 32 main parameters. (6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11), (5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17), (5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6, ∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11), (5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13) Not many precise upper bounds on these parameters have been obtained as yet, even for restricted subclasses in P5. In 2018, Borodin, Ivanova, Kazak proved that every forbidding vertices of degree from 7 to 11 results in a tight description (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6). Recently, Borodin, Ivanova, and Kazak proved every 3-polytope in P5 with no vertices of degrees 6, 7, and 8 has a 5-vertex whose neighborhood is majorized by one of the sequences (5, 5, 5, 5, ∞) and (5, 5, 10, 5, 12), which is tight and improves a corresponding description (5, 5, 5, 5, ∞), (5, 5, 9, 5, 17), (5, 5, 10, 5, 14), (5, 5, 11, 5, 13) that follows from the Lebesgue Theorem. The purpose of this paper is to prove that every 3-polytope with minimum degree 5 and no vertices of degree 6 or 7 has a 5-vertex whose neighborhood is majorized by one of the ordered sequences (5, 5, 5, 5, ∞), (5, 5, 8, 5, 14), or (5, 5, 10, 5, 12).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 535-548
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

      Ta witryna wykorzystuje pliki cookies do przechowywania informacji na Twoim komputerze. Pliki cookies stosujemy w celu świadczenia usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Twoim komputerze. W każdym momencie możesz dokonać zmiany ustawień dotyczących cookies