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.
Maximum induced trees in graphs
✍ Scribed by Paul Erdös; Michael Saks; Vera T Sós
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 952 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## Abstract For a graph __G__, let __t__(__G__) denote the maximum number of vertices in an induced subgraph of __G__that is a tree. Further, for a vertex __v__∈__V__(__G__), let __t__(__G, v__) denote the maximum number of vertices in an induced subgraph of __G__that is a tree, with the extra cond
A study of the orders of maximal induced trees in a random graph G, with small edge probability p is given. In particular, it is shown that the giant component of almost every G,, where p = c/n and c > 1 is a constant, contains only very small maximal trees (that are of a specific type) and very lar