Permanent rank and transversals
نویسنده
چکیده
We use the polynomial method of Alon to give a sufficient condition for the existence of partial transversals in terms of the permanent rank of a certain matrix.
منابع مشابه
Faster Algorithms to Enumerate Hypergraph Transversals
A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k ≥ 3, our algorithms for hypergraphs of rank k, where the rank is the maximum size of a hyperedge, outperform the previous best. This also implies improved upper bounds on the maximu...
متن کاملOn the quasi-transversals of a matroid
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.
متن کاملLocal equivalence of transversals in matroids
Given any system of n subsets in a matroid M , a transversal of this system is an n-tuple of elements of M , one from each set, which is independent. Two transversals differing by exactly one element are adjacent, and two transversals connected by a sequence of adjacencies are locally equivalent, the distance between them being the minimum number of adjacencies in such a sequence. We give two s...
متن کاملA study of Nilpotent groups through right transversals
In group theory nilpotency of a group has a great importance. In this paper we have studied some concept of nilpotency through right transversals. We have also studied prime power groups and frattini subgroups through right transversals.
متن کاملPolynomial Time SAT Decision, Hypergraph Transversals and the Hermitian Rank
Combining graph theory and linear algebra, we study SAT problems of low “linear algebra complexity”, considering formulas with bounded hermitian rank. We show polynomial time SAT decision of the class of formulas with hermitian rank at most one, applying methods from hypergraph transversal theory. Applications to heuristics for SAT algorithms and to the structure of minimally unsatisfiable clau...
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:
- Australasian J. Combinatorics
دوره 53 شماره
صفحات -
تاریخ انتشار 2012