Abstract
We show that the problem whether a given simple graph G admits a quasi-covering to a fixed connected graph H is solvable in polynomial time if H has at most two vertices and that it is NP-complete otherwise.
As a byproduct we show constructions of regular quasi-covers and of multi-quasi-covers that might be of independent interest.
Supported by Charles University as GAUK 95710.
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References
Abello, J., Fellows, M.R., Stillwell, J.C.: On the complexity and combinatorics of covering finite complexes. Australian Journal of Combinatorics 4, 103–112 (1991)
Bílka, O., Lidický, B., Tesař, M.: Locally injective homomorphism to the simple Weight graphs. In: Ogihara, M., Tarui, J. (eds.) TAMC 2011. LNCS, vol. 6648, pp. 471–482. Springer, Heidelberg (2011)
Bodlaender, H.L.: The classification of coverings of processor networks. Journal of Parallel Distributed Computing 6, 166–182 (1989)
Fiala, J., Kratochvíl, J.: Complexity of partial covers of graphs. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 537–549. Springer, Heidelberg (2001)
Fiala, J., Kratochvíl, J.: Partial covers of graphs. Discussiones Mathematicae Graph Theory 22, 89–99 (2002)
Fiala, J., Kratochvíl, J., Pór, A.: On the computational complexity of partial covers of Theta graphs. Discrete Applied Mathematics 156, 1143–1149 (2008)
Fiala, J., Kratochvíl, J.: Locally injective graph homomorphism: Lists guarantee dichotomy. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 15–26. Springer, Heidelberg (2006)
Fiala, J., Kratochvíl, J.: Locally constrained graph homomorphisms — structure, complexity, and applications. Computer Science Review 2(2), 97–111 (2008)
Fiala, J., Paulusma, D.: A complete complexity classification of the role assignment problem. Theoretical Computer Science 349(1), 67–81 (2005)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co. Ltd. (1979)
Hell, P., Nešetřil, J.: On the complexity of H-colouring. Journal of Combinatorial Theory, Series B 48, 92–110 (1990)
Holyer, I.: The NP-completeness of edge-coloring. SIAM Journal on Computing 10(4), 718–720 (1981)
Kratochvíl, J., Proskurowski, A., Telle, J.A.: Covering regular graphs. Journal of Combinatorial Theory B 71, 1–16 (1997)
Kratochvíl, J., Proskurowski, A., Telle, J.A.: Covering directed multigraphs I. colored directed multigraphs. In: Möhring, R.H. (ed.) WG 1997. LNCS, vol. 1335, pp. 242–257. Springer, Heidelberg (1997)
Kratochvíl, J., Proskurowski, A., Telle, J.A.: Complexity of graph covering problems. Nordic Journal of Computing 5, 173–195 (1998)
Kristiansen, P., Telle, J.A.: Generalized H-coloring of graphs. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 456–466. Springer, Heidelberg (2000)
Lidický, B., Tesař, M.: Complexity of Locally Injective Homomorphism to the Theta Graphs. In: Iliopoulos, C.S., Smyth, W.F. (eds.) IWOCA 2010. LNCS, vol. 6460, pp. 326–336. Springer, Heidelberg (2011)
Matoušek, J., Nešetřil, J.: Invitation to Discrete Mathematics. Oxford University Press (2008)
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Fiala, J., Tesař, M. (2013). Dichotomy of the H-Quasi-Cover Problem. In: Bulatov, A.A., Shur, A.M. (eds) Computer Science – Theory and Applications. CSR 2013. Lecture Notes in Computer Science, vol 7913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38536-0_27
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DOI: https://doi.org/10.1007/978-3-642-38536-0_27
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