2014/05/05 by Raymond Hemmecke, Hemmecke, Raymond, Tobias Windisch +1 · 1 citation
Mathematics · #05C40 #05C81 #13P10 #13P25 #62H17 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Statistics Theory (math.ST) #math.AC #math.CO #math.ST #msc:05C40 #msc:05C81 #msc:13P10 #msc:13P25 #msc:62H17 #stat.TH
paper · pdf · doi:10.48550/arxiv.1405.0812
arxiv created 2015/01/19 · arxiv updated 2015/01/20
We consider the connectivity of fiber graphs with respect to Gröbner basis and Graver basis moves. First, we present a sequence of fiber graphs using moves from a Gröbner basis and prove that their edge-connectivity is lowest possible and can have an arbitrarily large distance from the minimal degree. We then show that graph-theoretic properties of fiber graphs do not depend on the size of the right-hand side. This provides a counterexample to a conjecture of Engström on the node-connectivity of fiber graphs. Our main result shows that the edge-connectivity in all fiber graphs of this counterexample is best possible if we use moves from Graver basis instead.