Maximum Induced Linear Forests in Outerplanar Graphs
β Scribed by Michael J. Pelsmajer
- Publisher
- Springer Japan
- Year
- 2004
- Tongue
- English
- Weight
- 340 KB
- Volume
- 20
- 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
## 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
We provide a formula for the number of edges of a maximum induced matching in a graph. As applications, we give some structural properties of (k + 1 )K2-free graphs, construct all 2K2-free graphs, and count the number of labeled 2K2-free connected bipartite graphs.