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Partitioning planar graphs without 4-cycles and 5-cycles into two forests with a specific condition.
- Source :
-
Discrete Applied Mathematics . Jan2024, Vol. 342, p347-354. 8p. - Publication Year :
- 2024
-
Abstract
- Let A be the family of planar graphs without 4-cycles and 5-cycles. In 2013, Hill et al. proved that every graph G ∈ A has a partition dividing V (G) into three sets, where two of them are independent, and the other induces a graph with a maximum degree at most 3. In 2021 Cho, Choi, and Park conjectured that every graph G ∈ A has a partition dividing V (G) into two sets, where one set induces a forest, and the other induces a forest with a maximum degree at most 2. In this paper, we show that every graph G ∈ A has a partition dividing V (G) into two sets, where one set induces a forest, and the other induces a disjoint union of paths and subdivisions of K 1 , 3. The result improves the aforementioned result by Hill et al. and yields progress toward the conjecture of Cho, Choi, and Park. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PLANAR graphs
*LOGICAL prediction
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 342
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 173860046
- Full Text :
- https://doi.org/10.1016/j.dam.2023.10.002