Название: LOCKS AND FORBIDDEN CONFIGURATIONS IN 4-GRACEFUL TREES
Авторы: Baransky, V. A.; Nasyrov, I. A.; Senchonok, T. A.
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https://elar.urfu.ru/handle/10995/157784
| Название: | LOCKS AND FORBIDDEN CONFIGURATIONS IN 4-GRACEFUL TREES |
| Авторы: | Baransky, V. A. Nasyrov, I. A. Senchonok, T. A. |
| Дата публикации: | 2026 |
| Издатель: | N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences Ural Federal University named after the first President of Russia B.N. Yeltsin |
| Библиографическое описание: | Baransky V. A. LOCKS AND FORBIDDEN CONFIGURATIONS IN 4-GRACEFUL TREES / V. A. Baransky, I. A. Nasyrov, T. A. Senchonok. — Text : electronic // Ural Mathematical Journal. — 2026. — Volume 12. — № 1. — P. 26-44. |
| Аннотация: | Let f be a proper coloring of the vertices of a simple graph G into colors from the set of colors {1, 2,…,k}. A coloring f on the set of edges of a graph G induces a function f′(e) = |f(u) - f(v)|, where e = uv is an arbitrary edge of the graph G. A coloring f is called a k-graceful coloring of a graph G if f′ is an edge proper coloring of this graph. We will call a graph a k-graceful graph or, simply, graceful graph if it has a k-graceful coloring. In this paper, we continue the study of 4-graceful trees. We introduce the concept of a lock in a tree T with maximum vertex degree Δ = 3. A lock is a configuration H in T whose main property is the presence of two special vertices u and v such that for any 4-graceful colorings of T, the pair of vertices u and v has a unique coloring in the colors from the set {1, 2, 3, 4} up to duality. The main goals of this work are as follows: 1) to construct some simple locks and indicate procedures whose application to known locks generates new locks (see Theorem 1); 2) to use locks and nodal 1-components for finding forbidden configurations for 4-graceful trees (see Propositions 1 and 2, as well as Theorem 2). |
| Ключевые слова: | GRAPH TREE GRACEFUL COLORING OF A GRAPH 4-GRACEFUL TREES |
| URI: | https://elar.urfu.ru/handle/10995/157784 |
| Условия доступа: | Creative Commons Attribution License |
| Текст лицензии: | https://creativecommons.org/licenses/by/4.0/ |
| Идентификатор РИНЦ: | 91852790 |
| EDN: | UDMAUK |
| ISSN: | 2414-3952 |
| DOI: | 10.15826/umj.2026.1.003 |
| Источники: | Ural Mathematical Journal. 2026. Volume 12. № 1 |
| Располагается в коллекциях: | Ural Mathematical Journal |
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| Файл | Описание | Размер | Формат | |
|---|---|---|---|---|
| umj_2026_12_1_004.pdf | 262,2 kB | Adobe PDF | Просмотреть/Открыть |
Лицензия на ресурс: Лицензия Creative Commons
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