Maximum <Emphasis Type="Italic">k</Emphasis>-regular induced subgraphs

Independent sets, induced matchings and cliques are examples of regular induced subgraphs in a graph. In this paper, we prove that finding a maximum cardinality k-regular induced subgraph is an NP-hard problem for any fixed value of k. We propose a convex quadratic upper bound on the size of a k-regular induced subgraph and characterize those graphs for which this bound is attained. Finally, we extend the Hoffman bound on the size of a maximum 0-regular subgraph (the independence number) from k=0 to larger values of k.     

The Academic History of Literature and Art as a “ Disease of Interpretation”: On the Paradoxical Nature of Interdisciplinary Boundaries

This article represents an academic response to Professor Zhang Jiang’s article “On Imposed Interpretation” published in Russian in the journal October (no. 1, 2015). It argues that the problems observed by Zhang arise from the reality of Western literary criticism over the past decades, and are associated with the contention between philosophy and philology that had its orgins in the West’s Platonic heritage. In outlining the complex symbiotic relationship between the two disciplines in Western literary history, this article finds that two theoretical motive forces catalyzed the process: the “philologization of philosophy” and the “philosophization of philology.” The writer argues that based on a full understanding of the paradoxical relationship between philosophy and philology, which are distinct from and yet attracted to each other, contemporary literary criticism can adopt the principles of “practical conservatism” and “cutting back of methodologies” as a means of healing the ever worsening “disease of intepreretation” in literary history.     

Transversal Graphs for Partially Ordered Sets: Sequencing, Merging and Scheduling Problems

This paper introduces an approach to solving combinatorial optimization problems on partially ordered sets by the reduction to searching source-sink paths in the related transversal graphs. Different techniques are demonstrated in application to finding consistent supersequences, merging partially ordered sets, and machine scheduling with precedence constraints. Extending the approach to labeled partially ordered sets we also propose a solution for the smallest superplan problem and show its equivalence to the well studied coarsest regular refinement problem. For partially ordered sets of a fixed width the number of vertices in their transversal graphs is polynomial, so the reduction allows us easily to establish that many related problems are solvable in polynomial or pseudopolynomial time. For example, we establish that the longest consistent supersequence problem with a fixed number of given strings can be solved in polynomial time, and that the precedence-constrained release-date maximum- or total-cost preemptive or nonpreemptive job-shop scheduling problem with a fixed number of jobs can be solved in pseudopolynomial time. We also show that transversal graphs can be used to generalize and strengthen similar results obtained earlier by dynamic programming.