Homomorphism-Homogeneous Partially Ordered Sets

Mašulović, Dragan

doi:10.1007/s11083-007-9069-x

Cited by 32 publications

(40 citation statements)

References 2 publications

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“…Recently there have been several results on homomorphism-homogeneous partially ordered sets. Cameron and Lockett [1] as well as Mašulović [7] both treat this topic. They classify homomorphismhomogeneous posets for strict and non-strict homomorphism, when the morphisms considered are homomorphisms, monomorphisms and isomorphisms.…”

Section: Introductionmentioning

confidence: 99%

Homomorphism–homogeneous graphs

Rusinov

Schweitzer

2010

Journal of Graph Theory

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We answer two open questions posed by Cameron and Nesetril concerning homomorphismhomogeneous graphs. In particular we show, by giving a characterization of these graphs, that extendability to monomorphism or to homomorphism leads to the same class of graphs when defining homomorphism-homogeneity.Further we show that there are homomorphism-homogeneous graphs that do not contain the Rado graph as a spanning subgraph answering the second open question. We also treat the case of homomorphism-homogeneous graphs with loops allowed, showing that the corresponding decision problem is co-NP complete. Finally we extend the list of considered morphism-types and show that the graphs for which monomorphisms can be extended to epimorphisms are complements of homomorphism homogeneous graphs.

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Section: Introductionmentioning

confidence: 99%

Homomorphism–homogeneous graphs

Rusinov

Schweitzer

2010

Journal of Graph Theory

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“…It is known (cf. [28,7]) that (Q, ≤) is homomorphism-homogeneous. Thus, the class of finite linear orders has the HAP.…”

Section: Automatic Homeomorphicitymentioning

confidence: 99%

“…Thus, the class of finite strict partial orders has the HAP. • By [7, Proposition 25] and[28, Theorem 4.5], we have that the structure (Q, ≤) is homomorphism-homogeneous. Thus, the class of finite linear orders has the HAP.…”

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confidence: 99%

On automatic homeomorphicity for transformation monoids

Pech

2015

Monatsh Math

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Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if every monoid-isomorphism of $\mathfrak{M}$ to the endomorphism monoid of a member of $\mathcal{K}$ is automatically a homeomorphism. In this paper we show automatic homeomorphicity-properties for the monoid of non-decreasing functions on the rationals, the monoid of non-expansive functions on the Urysohn space and the endomorphism-monoid of the countable universal homogeneous poset.Comment: 21 page

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“…In several recent papers [2,5,10,12] homomorphism-homogeneous relational structures such as graphs, tournaments and partially ordered sets have been investigated. As far as algebras are concerned, [4] contains the description of homomorphism-homogeneous lattices, together with some initial results concerning homomorphism-homogeneous semilattices.…”

Section: Introductionmentioning

confidence: 99%

Homomorphism-homogeneous monounary algebras

Jungábel

Mašulović

2013

Mathematica Slovaca

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ABSTRACT. In 2006, P. J. Cameron and J. Nešetřil introduced the following variant of homogeneity: we say that a structure is homomorphism-homogeneous if every homomorphism between finitely generated substructures of the structure extends to an endomorphism of the structure. In several recent papers homomorphism-homogeneous objects in some well-known classes of algebras have been investigated (e.g. lattices and semilattices), while finite homomorphismhomogeneous groups were described in 1979 under the name of finite quasiinjective groups. In this paper we characterize homomorphism-homogenous monounary algebras of arbitrary cardinalities.

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Homomorphism-Homogeneous Partially Ordered Sets

Cited by 32 publications

References 2 publications

Homomorphism–homogeneous graphs

Homomorphism–homogeneous graphs

On automatic homeomorphicity for transformation monoids

Homomorphism-homogeneous monounary algebras

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