Circuit-Difference Matroids
نویسندگان
چکیده
منابع مشابه
Circuit and fractional circuit covers of matroids
LetM be a connectedmatroid having a ground set E. Lemos andOxley proved that |E(M)| ≤ 2 c(M)c (M)where c(M) (resp. c(M)) is the circumference (resp. cocircumference) of M. In addition, they conjectured that one can find a collection of at most c(M) circuits which cover the elements ofM at least twice. In this paper, we verify this conjecture for regular matroids. Moreover, we show that a versio...
متن کاملOn the circuit-spectrum of binary matroids
Murty, in 1971, characterized the connected binary matroids with all circuits having the same size. We characterize the connected binary matroids with circuits of two different sizes, where the largest size is odd. As a consequence of this result we obtain both Murty’s result and other results on binary matroids with circuits of only two sizes. We also show that it will be difficult to complete...
متن کاملCircuit Admissible Triangulations of Oriented Matroids
All triangulations of euclidean oriented matroids are of the same PLhomeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PLspheres. For non-euclidean oriented matroids this question is wide open. One key point in the p...
متن کاملMatroids with the Circuit Cover Property
We verify a conjecture of P. Seymour (Europ. J. Combinatorics 2, p. 289) regarding circuits of a binary matroid. A circuit cover of a integer-weighted matroid (M; p) is a list of circuits of M such that each element e is in exactly p(e) circuits from the list. We characterize those binary matroids for which two obvious necessary conditions for a weighting (M; p) to have a circuit cover are also...
متن کاملMatroids with an infinite circuit-cocircuit intersection
We construct some matroids that have a circuit and a cocircuit with infinite intersection. This answers a question of Bruhn, Diestel, Kriesell, Pendavingh and Wollan. It further shows that the axiom system for matroids proposed by Dress does not axiomatize all infinite matroids. We show that one of the matroids we define is a thin sums matroid whose dual isn’t a thin sums matroid.
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: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/9314