On infinite antichains of matroids

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35951

Ding, G

Robertson and Seymour have shown that there is no infinite set of graphs in which no member is a minor of another. By contrast, it is well known that the class of all matroids does contain such infinite antichains. However, for many classes of matroids, even the class of binary matroids, it is not known whether or not the class contains an infinite antichain. Here, we examine a class of matroids of relatively simple structure: M{sub a,b,c} consists of those matroids for which the deletion of some set of at most a elements and the contraction of some set of at most b elements results in a matroid in which every component has at most c elements. We determine precisely when M{sub a,b,c} contains an infinite antichain. We also show that, among the matroids representable over a finite fixed field, there is no infinite antichain in a fixed M{sub a,b,c}; nor is there an infinite antichain when the circuit size is bounded.

• OSTI ID: 35951
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
LINEAR PROGRAMMING
MATRICES
NUMERICAL SOLUTION
PARAMETRIC ANALYSIS