On ternary transversal matroids
β Scribed by James G Oxley
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 806 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The purpose of this paper is to answer a question of Ingleton by characterizing the class of ternary transversal matroids.
π SIMILAR VOLUMES
Let M and N be ternary matroids having the same rank and the same ground set, and assume that every independent set in N is also independent in M. The main result of this paper proves that if M is 3-connected and N is connected and non-binary, then M = N . A related result characterizes precisely wh
We show that the set of r-quasi-transversals of a matroid, if nonempty, is the set of bases of a matroid. We also give an alternative proof of the known theorem which identifies the conjugate of the rank partition of a matroid.
The basis pair graph of a matroid on the ground set S has, as its vertices, ordered triples of the form (&, &, &), where B, and B2 are disjoint bases and B3 = S\(B, U 4). Two such vertices, (AI, AZ, As) and (Ri, B,, IQ, are adjacent if (B,, &, B3) can be obtained from (AI, A\*, As) by interchanging
We present an elementary proof of the well-known theorem of E&nor& and Fkdkerson that a matroid is a matching matroid if and only if it is transversal. Suppose G = (V, E) is a simple graph. It is well-known that match(G), the collection of all X C V which are covered by some matching in G, is the sy