منابع مشابه
Homomorphism-homogeneous graphs
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 ...
متن کاملHomomorphism-homogeneous Graphs with Loops
In 2006, P. J. Cameron and J. Nešetřil introduced the following variant of homogeneity: we say that a structure is homomorphismhomogeneous if every homomorphism between finite substructures of the structure extends to an endomorphism of the structure. In this paper we classify finite homomorphism-homogeneous graphs where some vertices may have loops, but only up to a certain point. We focus on ...
متن کاملHomomorphism-Homogeneous Relational Structures
We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterisations of countable graphs and posets with this property; an analogue of Fraı̈ssé’s Theorem; and representations of monoids as endomorphism monoids of such structures. ∗This...
متن کاملHomomorphism bounded classes of graphs
A class C of graphs is said to be H-bounded if each graph in the class C admits a homomorphism to H. We give a general necessary and sufficient condition for the existence of bounds with special local properties. This gives a new proof of Häggkvist-Hell theorem [5] and implies several cases of the existence of triangle free bounds for planar graphs.
متن کاملFinite Homomorphism-Homogeneous Permutations via Edge Colourings of Chains
A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation b...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2010
ISSN: 0364-9024
DOI: 10.1002/jgt.20478