Journal article

# All-Path Convexity: Two Characterizations, General Position Number, and One Algorithm

#### Year:

2024#### Published in:

Discrete Mathematics Lettersall-path convexity

Interval space

block graph

gated set

general position number

We present two characterizations for the all-path convex sets in graphs. Using the first criterion, we obtain a new characterization of connected block graphs and compute the general position number in a graph with respect to the all-path convexity. The second criterion allows us to provide a new algorithm for testing a set on all-path convexity.