49 citations · 62 across the 16 of their papers we have counts for
13 papers · 1 filter
Diameter and Length of Metric Graphs
Hee-Kap Ahn, Sergio Cabello, Otfried Cheong +2
A metric graph is a metric space obtained from a finite collection of intervals whose endpoints are identified in groups. It can also be seen as a finite, edge-weighted graph where…
The Borsuk number of a graph
José Cáceres, Delia Garijo, Alberto Márquez +1
The Borsuk problem asks for the smallest number of subsets with strictly smaller diameters into which any bounded set in the -dimensional space can be decomposed. It is a classi…
Homomorphisms between graphs embedded on surfaces
Delia Garijo, Andrew Goodall, Lluís Vena
We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the…
Shortcut sets for the locus of plane Euclidean networks
José Cáceres, Delia Garijo, Antonio González +3
We study the problem of augmenting the locus of a plane Euclidean network by inserting iteratively a finite set of segments, called \emph{shortcu…
Resolving sets for breaking symmetries of graphs
Delia Garijo, Antonio González, Alberto Márquez
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to u…
The resolving number of a graph
Delia Garijo, Antonio González, Alberto Márquez
We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important…