## Rucidski, A., Matching and covering the vertices of a random graph by copies of a given graph, Discrete Mathematics 105 (1992) 185-197. In this paper we partially answer the question: how slowly must p(n) converge to 0 so that a random graph K(n, p) has property PM, almost surely, where PM, me
Coverings and matchings of the vertices of a graph by the edges
β Scribed by G.Ts. Akopyan
- Publisher
- Elsevier Science
- Year
- 1974
- Weight
- 706 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0041-5553
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π SIMILAR VOLUMES
We prove that every connected graph on n vertices can be covered by at most nΓ2+O(n 3Γ4 ) paths. This implies that a weak version of a well-known conjecture of Gallai is asymptotically true.
Consider a collection of disjoint paths in graph G such that every vertex is on one of these paths. The size of the smallest such collection is denoted i(G). A procedure for forming such collections is established. Restricting attention to trees, the range of values for the sizes of the collections
The main theorem of that paper is the following: let G be a graph of order n, of size at least (nZ -3n + 6 ) / 2 . For any integers k, n,, n2,. . . , nk such that n = n, + n2 + ... + nk and n, 2 3, there exists a covering of the vertices of G by disjoint cycles (C,),=,..,k with ICjl = n,, except whe
The following problem is investigated. Given an undirected graph G, determine the smallest cardinality of a vertex set that meets all complete subgraphs KC G maximal under inclusion.