$n$-functionality of graphs

Volume 90 / 2001

Konrad Pi/oro Colloquium Mathematicum 90 (2001), 269-275 MSC: 04A05, 05C20, 05C78, 05C99. DOI: 10.4064/cm90-2-6


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.


  • Konrad Pi/oroInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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