Discussiones
Mathematicae Graph Theory 23(1) (2003) 5-21
DOI: https://doi.org/10.7151/dmgt.1182
BALANCED PROBLEMS ON GRAPHS WITH CATEGORIZATION OF EDGES
Stefan Berezný
Air Force Academy of M.R. Stefánik, Košice |
Vladimír Lacko
Institute of Mathematics |
Abstract
Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S1,... ,Sp is given. We consider optimization problems P on G defined by a family of feasible sets D(G) and the following objective function:
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For an arbitrary number of categories we show that the L5-perfect matching, L5-a-b path, L5-spanning tree problems and L5-Hamilton cycle (on a Halin graph) problem are NP-complete.
We also summarize polynomiality results concerning above objective functions for arbitrary and for fixed number of categories.
Keywords: algorithms on graphs, categorization of edges, NP-completeness.
2000 Mathematics Subject Classification: 05C85, 90C27, 68Q17.
References
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Received 18 December 2000
Revised 6 May 2002
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