Abstract
A graph G is (k, l) if its vertex set can be partitioned into at most k independent sets and l cliques. The (k, l)-Graph Sandwich Problem asks, given two graphs G 1 = (V,E 1) and G 2 = (V,E 2), whether there exists a graph G = (V,E) such that E 1 ⊆ E ⊆ E 2 and G is (k, l). In this paper, we prove that the (k, l)-Graph Sandwich Problem is NPcomplete for the cases k = 1 and l = 2; k = 2 and l = 1; or k = l = 2. This completely classifies the complexity of the (k, l)-Graph Sandwich Problem as follows: the problem is NP-complete, if k+l > 2; the problem is polynomial otherwise. In addition, we consider the degree Δ constraint subproblem and completely classifies the problem as follows: the problem is polynomial, for k ≤2 or ⊆≤3; the problem is NP-complete otherwise.
This research was partially supported by CNPq, MCT/FINEP PRONEX Project 107/97, CAPES (Brazil)/COFECUB (France) Project number 213/97, FAPERJ and ROCIÊNCIA-UERJ Project.
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Dantas, S., de Figueiredo, C.M., Faria, L. (2002). On the Complexity of (k, l)-Graph Sandwich Problems. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_9
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DOI: https://doi.org/10.1007/3-540-36379-3_9
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