Duality pairs and homomorphisms to oriented and un-oriented cycles

by   Santiago Guzmán-Pro, et al.

In the homomorphism order of digraphs, a duality pair is an ordered pair of digraphs (G,H) such that for any digraph, D, G→ D if and only if D↛H. The directed path on k+1 vertices together with the transitive tournament on k vertices is a classic example of a duality pair. This relation between paths and tournaments implies that a graph is k-colourable if and only if it admits an orientation with no directed path on more than k-vertices. In this work, for every undirected cycle C we find an orientation C_D and an oriented path P_C, such that (P_C,C_D) is a duality pair. As a consequence we obtain that there is a finite set, F_C, such that an undirected graph is homomorphic to C, if and only if it admits an F_C-free orientation. As a byproduct of the proposed duality pairs, we show that if T is a tree of height at most 3, one can choose a dual of T of linear size with respect to the size of T.



There are no comments yet.


page 1

page 2

page 3

page 4


Duality pairs and homomorphisms to oriented and unoriented cycles

In the homomorphism order of digraphs, a duality pair is an ordered pair...

Orientations without forbidden patterns on three vertices

Given a set of oriented graphs F, a graph G is an F-graph if it admits a...

Upward Point Set Embeddings of Paths and Trees

We study upward planar straight-line embeddings (UPSE) of directed trees...

Rooting for phylogenetic networks

This paper studies the relationship between undirected (unrooted) and di...

AOT: Pushing the Efficiency Boundary of Main-memory Triangle Listing

Triangle listing is an important topic significant in many practical app...

Enumeration of Preferred Extensions in Almost Oriented Digraphs

In this paper, we present enumeration algorithms to list all preferred e...

On dually-CPT and strong-CPT posets

A poset is a containment of paths in a tree (CPT) if it admits a represe...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.