منابع مشابه
Gaps in full homomorphism order
We characterise gaps in the full homomorphism order of graphs.
متن کاملAntichains in the homomorphism order of graphs
Denote by G and D, respectively, the the homomorphism poset of the finite undirected and directed graphs, respectively. A maximal antichain A in a poset P splits if A has a partition (B, C) such that for each p ∈ P either b ≤P p for some b ∈ B or p ≤p c for some c ∈ C. We construct both splitting and non-splitting infinite maximal antichains in G and in D. A point y ∈ P is a cut point in a pose...
متن کاملSplitting finite antichains in the homomorphism order
A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.
متن کاملOn the Homomorphism Order of Labeled Posets
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...
متن کاملFractal property of the graph homomorphism order
We show that every interval in the homomorphism order of finite undirected graphs is either universal or a gap. Together with density and universality this “fractal” property contributes to the spectacular properties of the homomorphism order. We first show the fractal property by using Sparse Incomparability Lemma and then by a more involved elementary argument.
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2017
ISSN: 1571-0653
DOI: 10.1016/j.endm.2017.06.070