P-matrix recognition is co-NP-complete

This is a summary of the proof by G.E. Coxson that P-matrix recognition is co-NP-complete. The result follows by a reduction from the MAX CUT problem using results of S. Poljak and J. Rohn.Comment: 9 page

Ramsey Properties of Permutations

The age of each countable homogeneous permutation forms a Ramsey class. Thus, there are five countably infinite Ramsey classes of permutations.Comment: 10 pages, 3 figures; v2: updated info on related work + some other minor enhancements (Dec 21, 2012

On Ramsey properties of classes with forbidden trees

Let F be a set of relational trees and let Forbh(F) be the class of all structures that admit no homomorphism from any tree in F; all this happens over a fixed finite relational signature $\sigma$. There is a natural way to expand Forbh(F) by unary relations to an amalgamation class. This expanded class, enhanced with a linear ordering, has the Ramsey property.Comment: Keywords: forbidden substructure; amalgamation; Ramsey class; partite method v2: changed definition of expanded class; v3: final versio

Homomorphisms and Structural Properties of Relational Systems

Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.Comment: PhD Thesis, 77 pages, 14 figure

Adjoint functors and tree duality

A family T of digraphs is a complete set of obstructions for a digraph H if for an arbitrary digraph G the existence of a homomorphism from G to H is equivalent to the non-existence of a homomorphism from any member of T to G. A digraph H is said to have tree duality if there exists a complete set of obstructions T consisting of orientations of trees. We show that if H has tree duality, then its arc graph delta H also has tree duality, and we derive a family of tree obstructions for delta H from the obstructions for H. Furthermore we generalise our result to right adjoint functors on categories of relational structures. We show that these functors always preserve tree duality, as well as polynomial CSPs and the existence of near-unanimity functions.Comment: 14 pages, 2 figures; v2: minor revision

Interleaved adjoints on directed graphs

For an integer k >= 1, the k-th interlacing adjoint of a digraph G is the digraph i_k(G) with vertex-set V(G)^k, and arcs ((u_1, ..., u_k), (v_1, ..., v_k)) such that (u_i,v_i) \in A(G) for i = 1, ..., k and (v_i, u_{i+1}) \in A(G) for i = 1, ..., k-1. For every k we derive upper and lower bounds for the chromatic number of i_k(G) in terms of that of G. In particular, we find tight bounds on the chromatic number of interlacing adjoints of transitive tournaments. We use this result in conjunction with categorial properties of adjoint functors to derive the following consequence. For every integer ell, there exists a directed path Q_{\ell} of algebraic length ell which admits homomorphisms into every directed graph of chromatic number at least 4. We discuss a possible impact of this approach on the multifactor version of the weak Hedetniemi conjecture

Dualities and Dual Pairs in Heyting Algebras

We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categorie

Combinatorial Characterizations of K-matrices

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids. As an application, we show that a simple principal pivot method applied to the linear complementarity problems with K-matrices converges very quickly, by a purely combinatorial argument.Comment: 17 pages; v2, v3: clarified proof of Thm 5.5, minor correction

Post-synthetic derivatization of graphitic carbon nitride with methanesulfonyl chloride: Synthesis, characterization and photocatalysis

Bulk graphitic carbon nitride (CN) was synthetized by heating of melamine at 550 degrees C, and the exfoliated CN (ExCN) was prepared by heating of CN at 500 degrees C. Sulfur-doped CN was synthesized by heating of thiourea (S-CN) and by a novel procedure based on the post-synthetic derivatization of CN with methanesulfonyl (CH3SO2-) chloride (Mes-CN and Mes-ExCN). The obtained nanomaterials were investigated by common characterization methods and their photocatalytic activity was tested by means of the decomposition of acetic orange 7 (AO7) under ultraviolet A (UVA) irradiation. The content of sulfur in the modified CN decreased in the sequence of Mes-ExCN > Mes-CN > S-CN. The absorption of light decreased in the opposite manner, but no influence on the band gap energies was observed. The methanesulfonyl (mesyl) groups connected to primary and secondary amine groups were confirmed by high resolution mass spectrometry (HRMS). The photocatalytic activity decreased in the sequence of Mes-ExCN > ExCN > CN approximate to Mes-CN > S-CN. The highest activity of Mes-ExCN and ExCN was explained by the highest amounts of adsorbed Acetic Orange 7 (AO7). In addition, in the case of Mes-ExCN, chloride ions incorporated in the CN lattice enhanced the photocatalytic activity as well.Web of Science102art. no. 19

Pivoting in Linear Complementarity: TwoPolynomial-Time Cases

We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty's least-index pivot rule (under any fixed index order) leads to a quadratic number of iterations on Morris's highly cyclic P-LCP examples. We then show that on K-matrix LCP instances, all pivot rules require only a linear number of iterations. As the main tool, we employ unique-sink orientations of cubes, a useful combinatorial abstraction of the P-LC