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We give a constructive characterization of undirected graphs which contain k spanning trees after adding any new edge. This is a generalization of a theorem of Henneberg and Laman who gave the characterization for k=2. We also give a constructive characterization of graphs which have k edge-disjoint spanning trees after deleting any edge of them.
Bibtex entry:
AUTHOR | = | {Frank, Andr{\'a}s and Szeg{\H o}, L{\'a}szl{\'o}}, |
TITLE | = | {Constructive characterizations for packing and covering with trees (Revised version of TR-2001-05)}, |
NOTE | = | {{\tt egres.elte.hu}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2002}, |
NUMBER | = | {TR-2002-05} |