In this paper we define the notion of an f(k)-uniform parameterized exponential time scheme. We show that a problem can be solved in parameterized O(2o(f(k)) p(n)) time if and on...
We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating matchings of planar graphs, up to matrix operations on their rows and columns. If such a matrix is ...
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
We show that computing the lexicographically first four-coloring for planar graphs is p 2hard. This result optimally improves upon a result of Khuller and Vazirani who prove this ...
We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property π is called a π-graph. If π satis...