Let S be a finite set and M = (S, B) be a matroid where B is the set of its bases. We say that a basis B is greedy in M or the pair (M, B) is greedy if, for every sum of bases vector w, the coefficient: where B and its characteristic vector will not be distinguished, is integer. We define a notion
On matroids induced by packing subgraphs
β Scribed by Martin Loebl; Svatopluk Poljak
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 959 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
Let M be a matroid on a finite set E(M). Then M is packable by bases if E(M) is the disjoint union of bases. A partial packing of M is a collection of disjoint bases whose union is a proper subset of E(M). M is a randomly packable by bases if every partial packing can be extended to a packing of M.
If G is a block, then a vertex u of G is called critical if Gu is not a block. In this article, relationships between the localization of critical vertices and the localization of vertices of relatively small degrees (especially, of degree two) are studied. A block is called semicritical if a) each
Solving a problem of Alon, we prove that every graph G on n vertices with 6(G) 2 1 contains an induced subgraph H such that all the degrees in H are odd and 1 V(H)\ >(l -o(l))Jn/6.