On the sum of matroids, III
✍ Scribed by András Recski
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 796 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
Almost
irreducible graphic matroids are characterized and the structure of all the possible decompositions of a graphic matroid 1 into the sum of matroids is described (provided that Y is connected and not a single circuit). Some contributions to the solvability of the matroid equation JB vZ=iu are also obtained.
📜 SIMILAR VOLUMES
We discuss a composition operation of delta-matroids, called delta-sum, in relation to similar compositions of related combinatorial structures like matroids and jump systems. The delta-sum of matching delta-matroids is associated with the linkings of a graph. We exhibit a min-max formula for the po
We associate to a simple matroid (resp. a geometric lattice) \(M\) and a number \(d\) dividing the rank of \(M\) a partially ordered set \(\mathscr{L}_{d}(M)\) whose upper intervals are (set-) partition lattices. Indeed, for some important cases they are exponential structures in the sense of Stanle