## On constructive characterizations of (k,l)-sparse graphs

### Abstract

In this paper we study constructive characterizations of graphs satisfying tree-connectivity requirements. The main result is the following: if k and l are positive integers and l \leq k/2, then a necessary and sufficient condition is proved for a node beeing the last node of a construction in a graph having at most k|X|-(k+l) induced edges in every subset X of nodes.

Bibtex entry:

@techreport{egres-03-10,
AUTHOR = {Szeg{\H o}, L{\'a}szl{\'o}},
TITLE = {On constructive characterizations of $(k,l)$-sparse graphs},
NOTE= {{\tt www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2003},
NUMBER = {TR-2003-10}
}