28 research outputs found
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 . 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