منابع مشابه
Infinite Gammoids
Finite strict gammoids, introduced in the early 1970’s, are matroids defined via finite digraphs equipped with some set of sinks: a set of vertices is independent if it admits a linkage to these sinks. In particular, an independent set is maximal (i.e. a base) precisely if it is linkable onto the sinks. In the infinite setting, this characterization of the maximal independent sets need not hold...
متن کاملGammoids, Pseudomodularity and Flatness Degree
We introduce the concept of flatness degree for matroids, as a generalization of submodularity. This represents weaker variations of the concept of flatness which characterize strict gammoids for finite matroids. We prove that having flatness degree 3, which is the smallest non-trivial flatness degree, implies pseudomodularity on the lattice of flats of the matroid. We show however an example o...
متن کاملInfinite Gammoids: Minors and Duality
This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minor-closed. Also, we prove that finite-rank minors of gammoids are gammoids. Furthermore, the topological gammoids of Carmesin (2014) are proved to coincide, as matroids...
متن کاملForbidden-minors for splitting binary gammoids
In this paper, we obtain a forbidden-minor characterization of the class of binary gammoids M such that, for every pair of elements x, y of M, both the splitting matroid Mx,y and the element splitting matroid M ′ x,y are binary gammoids.
متن کاملUndirected Reachability
If we don’t consider the space constraint, we can solve this problem using standard DFS or BFS algorithms, which have running time O(|V | + |E|), but take space O(|V |). We are interested in algorithms that use space O(log n) and run in time poly(n). In particular, we can only store Θ(1) vertices, since each vertex description takes O(log n) bits where n is the total number of vertices. This le...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1984
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-120-1-1-5