Reachability-based matroid-restricted packing of arborescences
نویسندگان
چکیده
The fundamental result of Edmonds [5] started the area of packing arborescences and the great number of recent results shows increasing interest of this subject. Two types of matroid constraints were added to the problem in [2, 3, 9], here we show that both contraints can be added simultaneously. This way we provide a solution to a common generalization of the reachability-based packing of arborescences problem of the first author [14] and the matroid intersection problem of Edmonds [4].
منابع مشابه
Matroid-Based Packing of Arborescences
We provide the directed counterpart of a slight extension of Katoh and Tanigawa’s result [8] on rooted-tree decompositions with matroid constraints. Our result characterizes digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds’ result [1] on packing of spanning arborescences and implies – using a general orientation result of Frank [4] – the a...
متن کاملOn packing spanning arborescences with matroid constraint
Let D = (V + s,A) be a digraph with a designated root vertex s. Edmonds’ seminal result [4] implies that D has a packing of k spanning s-arborescences if and only if D has a packing of k (s, t)-paths for all t ∈ V , where a packing means arc-disjoint subgraphs. Let M be a matroid on the set of arcs leaving s. A packing of (s, t)-paths is called M-based if their arcs leaving s form a base of M w...
متن کاملCovering Intersecting Bi-set Families under Matroid Constraints
Edmonds’ fundamental theorem on arborescences [4] characterizes the existence of k pairwise edge-disjoint arborescences with the same root in a directed graph. In [9], Lovász gave an elegant alternative proof which became the base of many extensions of Edmonds’ result. In this paper, we use a modification of Lovász’ method to prove a theorem on covering intersecting bi-set families under matroi...
متن کاملIndependent and maximal branching packing in infinite matroid-rooted digraphs
We prove a common generalization of the maximal independent arborescence packing theorem of Cs. Király [13] (which itself is a common generalization of the reachability based arborescence packing result [12] and a matroid based arborescence packing result [5]) and two of our earlier works about packing branchings in infinite digraphs, namely [9] and [11].
متن کاملA note on disjoint arborescences
Recently Kamiyama, Katoh, and Takizawa have shown a theorem on packing arc-disjoint arborescences that is a proper extension of Edmonds’ theorem on disjoint spanning branchings. We show a further extension of their theorem, which makes clear an essential rôle of a reachability condition played in the theorem. The right concept required for the further extension is “convexity” instead of “reacha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016