Premium
MINTY COLORINGS AND ORIENTATIONS OF MATROIDS
Author(s) -
Bland Robert G.,
Vergnas Michel Las
Publication year - 1979
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1979.tb32777.x
Subject(s) - matroid , abstraction , property (philosophy) , combinatorics , characterization (materials science) , mathematics , discrete mathematics , physics , epistemology , philosophy , optics
S ummary Oriented matroids are known to have a Minty coloring property. We show here that this property characterizes oriented matroids. The proof is based upon another characterization of oriented matroids due to Bland and Las Vergnas [2]. The result indicates that oriented matroids provide the broadest possible abstraction of directed graphs and vector spaces over ordered fields as systems of signed sets.