منابع مشابه
The Erdös-Pósa property for matroid circuits
The number of disjoint cocircuits in a matroid is bounded by its rank. There are, however, matroids with arbitrarily large rank that do not contain two disjoint cocircuits; consider, for example, M(Kn) and Un,2n. Also the bicircular matroids B(Kn) have arbitrarily large rank and have no 3 disjoint cocircuits. We prove that for each k and n there exists a constant c such that, if M is a matroid ...
متن کاملDetermining a Binary Matroid from its Small Circuits
It is well known that a rank-r matroid M is uniquely determined by its circuits of size at most r. This paper proves that if M is binary and r > 3, then M is uniquely determined by its circuits of size at most r − 1 unless M is a binary spike or a special restriction thereof. In the exceptional cases, M is determined up to
متن کاملMatroid packing and covering with circuits through an element
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M , the sum of the maximum number of disjoint circuits and the minimum number of circuits needed to cover M is at most r∗(M) + 1. This paper considers the set Ce(M) of circuits through a fixed element e such that M/e is connected. Let νe(M) be the maximum size of a subset of Ce(M) in which any two distinct members meet o...
متن کاملRelaxations of the matroid axioms I: Independence, Exchange and Circuits
Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axio...
متن کاملA Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid
We provide a constructive characterisation of circuits in the simple (2, 2)sparsity matroid. A circuit is a simple graph G = (V,E) with |E| = 2|V | − 1 and the number of edges induced by any X ( V is at most 2|X| − 2. Insisting on simplicity results in the Henneberg operation being enough only when the graph is sufficiently connected. Thus we introduce 3 different sum operations to complete the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1986
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(86)80044-0