作者：Lourenco, Bruno F.; Roshchina, Vera; Saunderson, James
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; University of New South Wales Sydney; Monash University
摘要：Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or 'nice') which is, in turn, stronger than merely being facially exposed. Hyperbolicity cones are a family of algebraically structured closed convex cones that contain all spectrahedral cones (linear sections of positive semidefinite cones) as special cases. It is known that all spectrahedral cones are amenable. We establish that all hyperbolicity cones are amenable. As part of t...
作者：Ferhat, Dehia Ait; Kiraly, Zoltan; Sebo, Andras; Stauffer, Gautier
作者单位：Mentor Graphics Inc; Eotvos Lorand University; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Lausanne
摘要：Given an undirected graph, are there k matchings whose union covers all of its nodes, that is, a matching-k-cover? When k = 1, the problem is equivalent to the existence of a perfect matching for which Tutte's celebrated matching theorem (J. Lon. Math. Soc., 1947) provides a `good' characterization. We prove here, when k is greater than one, a `good' characterization a la Konig: for k >= 2, there exist k matchings covering every node if and only if for every stable set S, we have vertical bar ...
作者：Herings, P. Jean-Jacques; Zhan, Yang
作者单位：Tilburg University; Nanjing University; Nanjing University
