arXiv subjects
Publications and source records attributed to T. Kloks.
We show that there are polynomial-time algorithms to compute maximum independent sets in the categorical products of two cographs and two splitgraphs. We show that the ultimate categorical independence ratio is computable in polynomial time for cographs.
In memoriam N.G. de Bruijn. In this article I present some highlights of De Bruijn's contributions in combinatorics. This article does not survey his work on eg Penrose tilings, asymptotics or AUTOMATH; other surveys on these topics are being written by others.
The GG-width of a class of graphs GG is defined as follows. A graph G has GG-width k if there are k independent sets N1,...,Nk in G such that G can be embedded into a graph H in GG such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms. We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs.
Let k be a natural number. Let G be a graph and let N_1,...,N_k be k independent sets in G. The graph G is k-probe distance hereditary if G can be embedded into a DH-graph by adding edges between vertices that are contained in the same independent set. We show that there exists a polynomial-time algorithm to check if a graph G is k-probe distance hereditary.