8,576 research outputs found
Universal graphs with forbidden subgraphs and algebraic closure
We apply model theoretic methods to the problem of existence of countable
universal graphs with finitely many forbidden connected subgraphs. We show that
to a large extent the question reduces to one of local finiteness of an
associated''algebraic closure'' operator. The main applications are new
examples of universal graphs with forbidden subgraphs and simplified treatments
of some previously known cases
On the graph condition regarding the -inverse cover problem
In their paper titled "On -inverse covers of inverse monoids", Auinger and
Szendrei have shown that every finite inverse monoid has an -inverse cover
if and only if each finite graph admits a locally finite group variety with a
certain property. We study this property and prove that the class of graphs for
which a given group variety has the required property is closed downwards in
the minor ordering, and can therefore be described by forbidden minors. We find
these forbidden minors for all varieties of Abelian groups, thus describing the
graphs for which such a group variety satisfies the above mentioned condition
The complexity of the list homomorphism problem for graphs
We completely classify the computational complexity of the list H-colouring
problem for graphs (with possible loops) in combinatorial and algebraic terms:
for every graph H the problem is either NP-complete, NL-complete, L-complete or
is first-order definable; descriptive complexity equivalents are given as well
via Datalog and its fragments. Our algebraic characterisations match important
conjectures in the study of constraint satisfaction problems.Comment: 12 pages, STACS 201
Congruence modularity implies cyclic terms for finite algebras
An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar
Universal graphs with a forbidden subtree
We show that the problem of the existence of universal graphs with specified
forbidden subgraphs can be systematically reduced to certain critical cases by
a simple pruning technique which simplifies the underlying structure of the
forbidden graphs, viewed as trees of blocks. As an application, we characterize
the trees T for which a universal countable T-free graph exists
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