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

Authors:
László Szegö
Affiliations:
Department of Operations Research, Eötvös University, Budapest, Hungary
Venue:
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Year:
2006

Citing 4
Cited 0

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Constructive characterizations for packing and covering with trees

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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 ≤ k/2, then a necessary and sufficient condition is proved for a node being the last node of a construction in a graph having at most k|X|-(k+l) induced edges in every subset X of nodes. The arguments and proofs extend those of Frank and Szegö for the case l = 1 [A. Frank, L. Szegö, Constructive characterizations on packing and covering by trees, Discrete Appl. Math. 131 (2) (2003) 347-371].