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http://elar.urfu.ru/handle/10995/127439
Название: | AROUND THE ERDÖS–GALLAI CRITERION |
Авторы: | Baransky, V. A. Senchonok, T. A. |
Дата публикации: | 2023 |
Библиографическое описание: | Baransky V. A. AROUND THE ERDÖS–GALLAI CRITERION / V. A. Baransky, T. A. Senchonok. — Text : electronic // Ural Mathematical Journal. — 2023. — Volume 9. — № 1. — P. 29-48. |
Аннотация: | By an (integer) partition we mean a non-increasing sequence λ = (λ1,λ2,…) of non-negative integers that contains a finite number of non-zero components. A partition λ is said to be graphic if there exists a graph G such that λ = dptG, where we denote by dptG the degree partition of G composed of the degrees of its vertices, taken in non-increasing order and added with zeros. In this paper, we propose to consider another criterion for a partition to be graphic, the ht-criterion, which, in essence, is a convenient and natural reformulation of the well-known Erdös-Gallai criterion for a sequence to be graphical. The ht-criterion fits well into the general study of lattices of integer partitions and is convenient for applications. The paper shows the equivalence of the Gale-Ryser criterion on the realizability of a pair of partitions by bipartite graphs, the ht-criterion and the Erdös-Gallai criterion. New proofs of the Gale-Ryser criterion and the Erdös-Gallai criterion are given. It is also proved that for any graphical partition there exists a realization that is obtained from some splitable graph in a natural way. A number of information of an overview nature is also given on the results previously obtained by the authors which are close in subject matter to those considered in this paper. |
Ключевые слова: | INTEGER PARTITION THRESHOLD GRAPH BIPARTITE GRAPH BIPARTITE-THRESHOLD GRAPH FERRERS DIAGRAM |
URI: | http://elar.urfu.ru/handle/10995/127439 |
Условия доступа: | Creative Commons Attribution License |
Текст лицензии: | https://creativecommons.org/licenses/by/4.0/ |
Идентификатор РИНЦ: | 54265303 |
ISSN: | 2414-3952 |
DOI: | 10.15826/umj.2023.1.003 |
Источники: | Ural Mathematical Journal. 2023. Volume 9. № 1 |
Располагается в коллекциях: | Ural Mathematical Journal |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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umj_2023_9_1_004.pdf | 223,15 kB | Adobe PDF | Просмотреть/Открыть |
Лицензия на ресурс: Лицензия Creative Commons