Universal partial order represented by means of oriented trees and other simple graphs

Hubička, Jan; Nešetřil, Jaroslav

doi:10.1016/j.ejc.2004.01.008

Cited by 32 publications

(40 citation statements)

References 10 publications

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“…It is a well-known fact that the homomorphism order of (loopless) directed graphs is universal (see [20]; see also Hubička and Nešetřil's [11] simpler proof). The claim then follows from Propositions 3.1 and 3.3.…”

Section: Proposition 32 Let G Be a Graph Then P G Is A Core If Andmentioning

confidence: 99%

On the Homomorphism Order of Labeled Posets

Kwuida

Lehtonen

2010

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Abstract. Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.

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Section: Proposition 32 Let G Be a Graph Then P G Is A Core If Andmentioning

confidence: 99%

On the Homomorphism Order of Labeled Posets

Kwuida

Lehtonen

2010

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“…It is known (Corollary 3.11, [28]) that there are only two finite maximal antichains, both of size one, in G. The study of infinite antichains in G has centred around the notion of splitting (see for example [21]). The homomorphism order has been shown to be universal on various other classes of structures: digraphs ( [58], oriented paths and trees ( [33]), partial orders and lattices ( [47]). Locally constrained graph homomorphisms -i.e.…”

Section: Homomorphisms: Embeddings and Epimorphismsmentioning

confidence: 99%

Well quasi-order in combinatorics: embeddings and homomorphisms

Huczynska¹,

Ruškuc²

2015

Surveys in Combinatorics 2015

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The notion of well quasi-order (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between 'tame' and 'wild' such classes. In this article we survey such situations within combinatorics, and attempt to identify promising directions for further research. We argue that these are intimately linked with a more systematic and detailed study of homomorphisms in combinatorics.

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“…However note that here the key property is that objects are not connected and contains odd cycles of unbounded length. If we want to obtain connected graphs with bounded cycles then we have to refer to [4,13,5] where it is proved that that the class of finite oriented trees T and even the class of finite oriented paths form universal partial orders. These strong notions are not needed in this paper.…”

Section: Representing Divisibilitymentioning

confidence: 99%