7 citations · 29 across the 20 of their papers we have counts for
22 papers
Convex geometries and directed paths on three vertices
Júlio Araújo, Mitre C. Dourado, Marisa Gutierrez +2
A convexity space is an ordered pair , where is an arbitrary set and is a family of subsets of , called convex, which contains $\{\emptyset,V\…
Counting -convex sets in graphs
Mitre C. Dourado, Luciano N. Grippo, Min Chih Lin +1
We study the -convexity, the path convexity generated by all three-vertex paths, and focus on the problem of counting the -convex vertex sets of a graph , denoted by $…
The iteration time and the general position number in graph convexities
Julio Araujo, Mitre C. Dourado, Fábio Protti +1
In this paper, we study two graph convexity parameters: iteration time and general position number. The iteration time was defined in 1981 in the geodesic convexity, but its comput…
All-path convexity: Combinatorial and complexity aspects
Fábio Protti, João V. C. Thompson
Let be any collection of paths of a graph . For , define $I(S)=S\cup\{v\mid v \ \mbox{lies in a path of} \ ¶\ \mbox{with endpoints in} \ S\}$. Let $\C$ b…
Computing the hull and interval numbers in the weakly toll convexity
Mitre C. Dourado, Marisa Gutierrez, Fábio Protti +1
A walk of a graph is a \textit{weakly toll walk} if , implies , and implies $u_j=u…
Convex geometries over induced paths with bounded length
Marisa Gutierrez, Fábio Protti, Silvia B. Tondato
Graph convexity spaces have been studied in many contexts. In particular, some studies are devoted to determine if a graph equipped with a convexity space is a {\em convex geometry…