Paper Info
Title
Homomorphisms of planar (m, n)-colored-mixed graphs to planar targets
Abstract
An (m, n)-colored-mixed graph G = (V, A(1), A(2), ..., A(m), E-1, E-2, ..., E-n) is a graph having m colors of arcs and n colors of edges. We do not allow two arcs or edges to have the same endpoints. A homomorphism from an (m, n)-colored-mixed graph G to another (m, n) colored-mixed graph H is a morphism phi : V (G) -> V (H) such that each edge (resp. arc) of G is mapped to an edge (resp. arc) of H of the same color (and orientation). An (m, n)-colored-mixed graph T is said to be Pg(m,n)-universal if every graph in P-g((m,n))-(the planar (m, n)-colored-mixed graphs with girth at least g) admits a homomorphism to T. We show that planar P(m,n) g-universal graphs do not exist for 2m +n (and any value of g) and find a minimal (in the number vertices) planar P(m,n) g-universal graphs in the other cases. (C) 2021 Elsevier B.V. All rights reserved.
Year
DOI
Venue
2021
10.1016/j.disc.2021.112600
DISCRETE MATHEMATICS
Keywords
DocType
Volume
Homomorphism, Planar graphs, Mixed graphs
Journal
344
Issue
ISSN
Citations 
12
0012-365X
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Fabien Jacques100.34
Pascal Ochem225836.91