id: 01964611
dt: j
an: 01964611
au: Jani, Mahendra; Rieper, Robert G.; Zeleke, Melkamu
ti: Enumeration of $K$-trees and applications.
so: Ann. Comb. 6, No.3-4, 375-382 (2002).
py: 2002
pu: Birkhäuser Verlag (Springer), Basel
la: EN
cc: 
ut: $K$-trees; terminal edges; generating functions; generalized Catalan
    numbers; planted plane cacti
ci: 
li: 
ab: Summary: A $k$-tree is constructed from a single distinguished $k$-cycle by
    repeatedly gluing other $k$-cycles to existing ones along an edge. If
    $K$ is any nonempty subset of $\{2,3,4,\ldots\}$, then a $K$-tree is
    obtained as above using $k$-cycles with $k\in K$. In this paper, we
    enumerate ordered $K$-trees, show that the ratio of terminal edges to
    total number of edges in $k$-trees is $\frac{k-1}k$, and use the
    $K$-trees as models to enumerate planted plane cacti.
rv: