On the Connectivity of Fiber Graphs Fiber connectivity Gröbner basis Graver basis Fiber graph 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. Hemmecke, Raymond Windisch, Tobias 2015 2015-06-11 Article application/pdf islandora:1007814 http://hdl.handle.net/10560/islandora:1007814 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access