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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-2-6,
author = {Konrad Pi\'oro},
title = {n-functionality of graphs},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {269-275},
zbl = {0986.05052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-2-6}
}
Konrad Pióro. n-functionality of graphs. Colloquium Mathematicae, Tome 89 (2001) pp. 269-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-2-6/