2016/06/27 by Tara Fife, Fife, Tara, James Oxley +1 · 1 citation
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.1606.08354
A laminar family is a collection \mathscrA of subsets of a set E such that, for any two intersecting sets, one is contained in the other. For a capacity function c on \mathscrA, let \mathscrI be \I:|I∩ A| ≤ c(A)\text for all A∈\mathscrA\. Then \mathscrI is the collection of independent sets of a (laminar) matroid on E. We present a method of compacting laminar presentations, characterize the class of laminar matroids by their excluded minors, present a way to construct all laminar matroids using basic operations, and compare the class of laminar matroids to other well-known classes of matroids.