Maximum Δ\Delta-edge-colorable subgraphs of class II graphs

A graph $G$ is class II, if its chromatic index is at least $\Delta+1$. Let $H$ be a maximum $\Delta$-edge-colorable subgraph of $G$. The paper proves best possible lower bounds for $\frac{|E(H)|}{|E(G)|}$, and structural properties of maximum $\Delta$-edge-colorable subgraphs. It is shown that every set of vertex-disjoint cycles of a class II graph with $\Delta\geq3$ can be extended to a maximum $\Delta$-edge-colorable subgraph. Simple graphs have a maximum $\Delta$-edge-colorable subgraph such that the complement is a matching. Furthermore, a maximum $\Delta$-edge-colorable subgraph of a simple graph is always class I.Comment: 13 pages, 2 figures, the proof of the Lemma 1 is correcte

Police Violence and Corruption in the Philippines: Violent Exchange and the War on Drugs

In this article we explore the relationship between money and violence in the Philippine war on drugs. Building on long-term ethnographic and political engagement with a poor urban neighbourhood in Manila, we suggest that while the war on drugs has taken state killings to a new level, the Philippine state was no stranger to killing its own citizens before its onset. Furthermore, we argue that we cannot dissociate the killings from the rampant corruption in the Philippine police. By invoking the concept of violent exchange, the article shows that both corruption and death enter into particular understandings of state-citizen relationships. Because the war has reconfigured how death and corruption work, people in urban Manila are attempting desperately - as the stakes are high - to figure out how to engage with the police under these transforming conditions