We prove that, if M is a weakly 4-connected matroid with |E(M)| 7 and neither M nor M∗ is isomorphic to the cycle matroid of a ladder, then M has a proper minor M ′ such that M ′ is weakly 4-connected and |E(M ′)| |E(M)| − 2 unless M is some 12-element matroid with a special structure. © 2007 Elsevier Inc. All rights reserved.

The maximum intersection problem for a matroid and a greedoid, given by polynomial-time oracles, is shown NP -hard by expressing the satisfiability of boolean formulas in 3-conjunctive normal form as such an intersection. Also the corresponding approximation problem is shown NP -hard for certain approximation performance bounds. This is in contrast with the maximum matroid-matroid intersection ...

Let E be a possibly infinite set and let M N matroids defined on E. We say that the pair {M,N} has Intersection property if share an independent I admitting bipartition IM⊔IN such spanM(IM)∪spanN(IN)=E. The Matroid Conjecture of Nash-Williams says every matroid property. conjecture is known easy to prove in case when one uniform it was shown by Bowler Carmesin implied its special where direct s...

This paper presents the design and implementation of a real-time fuzzy-based artificial intelligence system for an interactive game. The chosen game is a remake of Pac-Man in which the opponents are BDI-style intelligent agents. The components of the system and the methods used in fuzzifying the game’s rules and variables are discussed. In addition, comparisons are drawn between the proposed fu...

For each proper minor-closed subclassM of the GF(q)representable matroids containing all GF(q)-representable matroids, we give, for all large r, a tight upper bound on the number of points in a rank-r matroid inM, and give a rank-r matroid inM for which equality holds. As a consequence, we give a tight upper bound on the number of points in a GF(q)-representable, rank-r matroid of large rank wi...

A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible hvectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question. We also prove the 1-dimensional case of a conjecture of Stanley that all matroid h-vectors are pure O-sequences. Finally, we completely characterize...