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DESCRIPTION: Tope graphs of Complexes of Oriented Matroids fall into the im
portant class of metric graphs called partial cubes. They capture a variety
of interesting graphs such as flip graphs of acyclic orientations of a gra
ph\, linear extension graphs of a poset\, region graphs of hyperplane arran
gements to name a few. After a soft introduction into oriented matroids and
tope graphs\, we give two purely graph theoretical characterizations of to
pe graphs of Complexes of Oriented Matroids. The first is in terms of a new
notion of excluded minors for partial cube\, the second is in terms of cla
ssical metric properties of certain so-called antipodal subgraphs. Corollar
ies include a characterization of topes of oriented matroids due to da Silv
a\, another one of Handa\, a characterization of lopsided systems due to La
wrence\, and an intrinsic characterization of tope graphs of affine oriente
d matroids. Moreover\, we give a polynomial time recognition algorithms for
tope graphs\, which solves a relatively long standing open question. I wil
l try to furthermore give some perspectives on classical problems as Las Ve
rgnas simplex conjecture in terms of Metric Graph Theory. Based on joint
work with H.-J\; Bandelt\, V. Chepoi\, and T. Marc.
DTSTAMP:20190424T132800
DTSTART:20190429T141500
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Kolja Knauer (Aix-Marseille Université): Tope graphs of (Complexes
of) Oriented Matroids
UID:95690609@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20190429-L-Knauer.html
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