Dejan Delic

Ryerson University · Department of Mathematics

In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over finite fields and reductions via absorbing subuniverses.

In this article, we provide a new algorithm for solving constraint satisfaction problems with Maltsev constraints, based on the new notion of Maltsev consistency.

One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language is either solvable in polynomial time or \textsc{NP}-complete. The conjecture was verified in certain special c...

It is well known that the constraint satisfaction problem over a general relational structure $\mathbb{A}$ is polynomial time equivalent to the constraint problem over some associated digraph. We present a variant of this construction and show that the corresponding constraint satisfaction problem is logspace equivalent to that over $\mathbb{A}$. M...

A subset 5 of vertices of a graph G is called a global connected dominating set if S is both a global dominating set and a connected dominating set. The global connected domination number is the minimum cardinality of a global connected dominating set of G and is denoted by γgc(G). In this paper, sharp bounds for γge are supplied, and all graphs at...

We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $G$ satisfies the connected existentially closed property and admits a homomorphism to $H$, then...

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace....

Let k be a positive integer, and let G=(V,E) be a graph with minimum degree at least k−1. A function f:V→{−1,1} is said to be a signed k-dominating function (SkDF) if ∑u∈N[v]f(u)⩾k for every v∈V. An SkDF f of a graph G is minimal if there exists no SkDF g such that g≠f and g(v)⩽f(v) for every v∈V. The maximum of the values of ∑v∈Vf(v), taken over a...

We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any non-trivial semigroup identity. We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R.

In this article we provide a complete classification of discriminator varieties of the form V(Kt), where K is a locally finite class of groups, closed under taking subgroups, which is contained in ApA2(p>2) and whose first-order theory is decidable.

We answer a question of Cameron's by giving examples of 2ℵ0 many non-isomorphic acyclic orientations of the infinite random graph with a topological ordering that do not have the pigeonhole property. Our examples also embed each countable linear ordering.

In this note we prove that the monoid End(R) of all endomorphisms of the random graph R is not simple. On the contrary, the lattice of ideals of End(R) embeds the poset of all subsets of , the set of natural numbers.

A graph G is inexhaustible if whenever a vertex of G is deleted the remaining graph is isomorphic to G. We address a question of Cameron [6], who asked which countable graphs are inexhaustible. In particular, we prove that there are continuum many countable inexhaustible graphs with properties in common with the infinite random graph, including adj...

A relational structure A satisfies the n k property if when- ever the vertex set of A is partitioned into n nonempty parts, the substruc- ture induced by the union of some k of the parts is isomorphic to A The 2 1 property is just the pigeonhole property, , introduced by P. Cameron in (5), and studied in (2) and (3). We classify the countable graph...

In this article the classification of finite flat graph algebras which have finite equational bases is given in terms of omitted induced subgraphs. The result is related to an earlier result obtained for finite graph algebras by Baker, McNulty, and Werner.

We construct a finitely based congruence-distributive variety of algebras in a finite language whose set of subalgebras of finite simple algebras is non-recursive.

. We show that End(R) is not regular and is not generated by its idempotents. The Rees order on the idempotents of End(R) has 2N0 many minimal elements. We also prove that the order type of Q is embeddable in the Rees order of End(R).

In this paper we construct a finitely based variety, whose equational theory is undecidable, yet whose word problems are recursively solvable, which solves a problem stated by G. McNulty (1992). The construction produces a discriminator variety with the aforementioned properties starting from a class of structures in some multisorted language (whic...

We study those relational structures S with the property (P) that each partition of S contains a block isomorphic to S. We show that the Fraïsse limits of parametric classes K. have property (P); over a binary language, every countable structure in K satisfying (P) along with a condition on 1-extensions must be isomorphic to this limit.

The class of width-two orders has a model companion. The model companion is complete, decidable, non-finitely axiomatizable, and has continuum many countable models. Generalizations of some results in (Pouzet, M., 1978, J. Combin. Theory Ser. B 25) are presented in the width-n case, for n2.