Stabilizing Weighted Graphs

An edge-weighted graph [Formula: see text] is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in network bargaining games and cooperative matching games, because they characterize instances that admit stable outcomes. We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm is combinatorial and exploits new structural properties of basic fractional matchings, which are of independent interest. In contrast, we show that the problem of finding a minimum cardinality subset of edges whose removal from a weighted graph G yields a stable graph, does not admit any constant-factor approximation algorithm, unless P = NP. In this setting, we develop an O(Δ)-approximation algorithm for the problem, where Δ is the maximum degree of a node in G.

Fissured Employment and Network Bargaining: Emerging Employment Relations Dynamics in a Contingent World of Work

For decades, direct employment relationships have been increasingly displaced by indirect employment relationships through networks of firms and layers of managerial control. The firm strategies driving these changes are organizational, geographic, and technological in nature and are facilitated by state policies. The resulting weakening of traditional forms of collective bargaining and worker power have led workers to counter by organizing broader alliances and complementing structural and associational power with symbolic power and state-oriented strategies through what the authors term “network bargaining.” These dynamics point to the limitations of dominant theories and frameworks for understanding employment relations and suggest a new approach that focuses on a range of direct and indirect work relationships, evolving forms of worker power, and networked patterns of worker–employer interactions.