Open problems on graph coloring for special graph classes.

For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c:V→{1,2,…}c:V→{1,2,…} such that c(u)≠c(v)c(u)≠c(v) for every edge uv∈Euv∈E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring

Minimum Fill-in of Sparse Graphs: {Kernelization} and Approximation

The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop kernelization algorithms for the problem on several classes of sparse graphs. We obtain linear kernels on planar graphs, and kernels of size in graphs excluding some fixed graph as a minor and in graphs of bounded degeneracy. As a byproduct of our results, we obtain approximation algorithms with approximation ratios on planar graphs and on H-minor-free graphs. These results significantly improve the previously known kernelization and approximation results for Minimum Fill-in on sparse graphs

On the parameterized complexity of finding separators with non-hereditary properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan 1985), while for example the problems of finding a minimum s-t separator that is a connected graph or an independent set are fixed-parameter tractable (Marx, O'Sullivan and Razgon, manuscript). We extend these results the following way: Finding a minimum c-connected s-t separator is FPT for c∈=∈2 and W[1]-hard for any c∈≥∈3. Finding a minimum s-t separator with diameter at most d is W[1]-hard for any d∈≥∈2. Finding a minimum r-regular s-t separator is W[1]-hard for any r∈≥∈1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. We also show that finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless NP ⊆ coNP/poly. © 2012 Springer-Verlag Berlin Heidelberg

A subexponential parameterized algorithm for proper interval completion

In the Proper Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into a proper interval graph, i.e., a graph admitting an intersection model of equal-length intervals on a line. The study of Proper Interval Completion from the viewpoint of parameterized complexity has been initiated by Kaplan, Shamir and Tarjan [FOCS 1994; SIAM J. Comput. 1999], who showed an algorithm for the problem working in O(16k⋅(n+m)) time. In this paper we present an algorithm with running time kO(k2/3)+O(nm(kn+m)), which is the first subexponential parameterized algorithm for Proper Interval Completion

Introduction to Queering the Whedonverses : Interrogating Whedon from a Multiplicity of Queer Perspectives

Over the last 15 years, Slayage: The Journal of Whedon Studies and other publications have featured a range of writing and scholarship about queer issues, identity, and representations related to the Whedonverses, but there has not yet been a publication dedicated solely to queer Whedon studies. This special issue, therefore, seemed timely, if not overdue

On Exact Algorithms for Treewidth

We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time ). This algorithm is based on the old dynamic programming method introduced by Held and Karp for the Traveling Salesman problem. We use some optimizations that do not a#ect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space used by the algorithm is an important factor to what input sizes the algorithm is e#ective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In thi