Deltas, extended odd holes and their blockers

Abstract

Let C be a clutter over ground set V where no element is contained in every member. We prove that if there is a w is an element of R-+(V) such that every member has weight greater than half the weight of V, then there must be a delta or the blocker of an extended odd hole minor. The proof of this result relies on a tool developed for finding delta or extended odd hole minors. (C) 2018 Elsevier Inc. All rights reserved.