- Tytuł:
- Alternating-Pancyclism in 2-Edge-Colored Graphs
- Autorzy:
-
Cordero-Michel, Narda
Galeana-Sánchez, Hortensia - Powiązania:
- https://bibliotekanauki.pl/articles/32222696.pdf
- Data publikacji:
- 2021-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
2-edge-colored graph
alternating cycle
alternating-pancyclic graph - Opis:
- An alternating cycle in a 2-edge-colored graph is a cycle such that any two consecutive edges have different colors. Let $ G_1, . . ., G_k $ be a collection of pairwise vertex disjoint 2-edge-colored graphs. The colored generalized sum of $ G_1, . . ., G_k $, denoted by $ \oplus_{i=1}^k G_i $, is the set of all 2-edge-colored graphs $G$ such that: (i) \( V(G)= \bigcup _{i=1}^k V(G_i) \), (ii) $ G \langle V(G_i) \rangle \cong G_i $ for $ i = 1, . . ., k $ where $ G \langle V(G_i) \rangle $ has the same coloring as $ G_i $ and (iii) between each pair of vertices in different summands of $G$ there is exactly one edge, with an arbitrary but fixed color. A graph $G$ in $\oplus_{i=1}^k G_i $ will be called a colored generalized sum (c.g.s.) and we will say that $ e \in E(G) $ is an exterior edge if and only if \( e \in E(G) \backslash ( \bigcup_{i=1}^k E(G_i)) \). The set of exterior edges will be denoted by $ E_\oplus $. A 2-edge-colored graph $G$ of order $2n$ is said to be an alternating-pancyclic graph, whenever for each $ l \in {2, . . ., n} $, there exists an alternating cycle of length $2l$ in $G$. The topics of pancyclism and vertex-pancyclism are deeply and widely studied by several authors. The existence of alternating cycles in 2-edge-colored graphs has been studied because of its many applications. In this paper, we give sufficient conditions for a graph $ G \in \oplus_{i=1}^k G_i $ to be an alternating-pancyclic graph.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 779-800
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł