Maximum induced forests of planar graphs
β Scribed by Jin Akiyama; Mamoru Watanabe
- Publisher
- Springer Japan
- Year
- 1987
- Tongue
- English
- Weight
- 80 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
Bounds are obtained for the number of vertices in a largest induced forest in a cubic graph with large girth. In particular, as girth increases without bound, the ratio of the number of vertices in a largest induced forest to the number of vertices in the whole graph approaches 3/4. The point arbof
Truszczydski, M., Decompositions of graphs into forests with bounded maximum degree, Discrete Mathematics 98 (1991) 207-222.
Let t(G) denote the cardinality of a maximum induced forest of a graph G with n vertices. For connected simple cubic graphs G without triangles, it is shown that r(G) 3 2n/3 except for two particular graphs. This lower bound is sharp and it improves a result due to J.A. Bondy, et al. [l]. Using this
## Abstract For a graph __G__, let __a__(__G__) denote the maximum size of a subset of vertices that induces a forest. Suppose that __G__ is connected with __n__ vertices, __e__ edges, and maximum degree Ξ. Our results include: (a) if Ξββ€β3, and __G__ββ β__K__~4~, then __a__(__G__)ββ₯β__n__βββe/4βββ1