$n$-functionality of graphs
Volume 90 / 2001
Colloquium Mathematicum 90 (2001), 269-275
MSC: 04A05, 05C20, 05C78, 05C99.
DOI: 10.4064/cm90-2-6
Abstract
We first characterize in a simple combinatorial way all finite graphs whose edges can be directed to form an $n$-functional digraph, for a fixed positive integer $n$. Next, we prove that the possibility of directing the edges of an infinite graph to form an $n$-functional digraph depends on its finite subgraphs only. These results generalize Ore's result for functional digraphs.
