On Disjoint Common Bases in Two Matroids
نویسندگان
چکیده
We prove two results on packing common bases of two matroids. First, we show that the computational problem of common base packing reduces to the special case where one of the matroids is a partition matroid. Second, we give a counterexample to a conjecture of Chow, which proposed a sufficient condition for the existence of a common base packing. Chow’s conjecture is a generalization of Rota’s basis conjecture.
منابع مشابه
On packing spanning trees in graphs and bases in matroids
We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We provide structural descriptions of such graphs and matroids. In the case of graphs, our results are relevant for certain communication protocols.
متن کاملA note on packing spanning trees in graphs and bases in matroids
We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We provide descriptions of such graphs and matroids, showing that such a graph (or matroid) has a unique decomposition. In the case of graphs, our results are releva...
متن کاملRota's Basis Conjecture for Paving Matroids
Rota conjectured that, given n disjoint bases of a rank-n matroid M , there are n disjoint transversals of these bases that are all bases of M . We prove a stronger statement for the class of paving matroids.
متن کاملDisjoint Bases for a Countable Family of Rank-finite Matroids
Let M = (Mr)reW be a system of matroids on a set S. For every transfinite sequence / of distinct elements of 5, we define a number TJ(/). In [12] we proved that the condition that r](f) 3=0 for every possible choice of/is necessary for M to have a system of mutually disjoint bases. Further, we showed that this condition is sufficient if R is countable and Mr is a rank-finite transversal matroid...
متن کاملSome inequalities for the Tutte polynomial
We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x + y = p lying in the positive quadrant. Every coloopless paving matroid is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases. For this latter class we give a proof that TM (a, a) ≤ max{TM (2a, 0), TM (0, 2a)} for a ≥ 2. We co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 25 شماره
صفحات -
تاریخ انتشار 2011