Abstract
Problems of recognition of product graphs and graph bundles with respect to Cartesian, categorical, strong and lexicographic product are considered. A short survey of results and open problems is given.
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J.Abello, M.R.Fellows and J.C.Stillwell: On the Complexity and Combinatorics of Covering Finite Complexes, Australasian Journal of Combinatorics 4 (1991) 103–112.
F.Aurenhammer, J.Hagauer and W.Imrich: Cartesian Graph Factorization at Logarithmic Cost per Edge, Computational Complexity 2 (1992) 331–349.
F.Aurenhammer, M.Formann, R.Idury, A.Schäffer and F.Wagner: Faster Isometric Embedding in Products of Complete Graphs, Discrete Applied Mathematics 52 (1994) 17–28.
T.Feder: Product Graph Representations, Journal of Graph Theory 16 (1992) 467–488.
J.Feigenbaum, J.Hershberger and A.A.Schäffer: A Polynomial Time Algorithm for Finding the Prime Factors of Cartesian-Product Graphs, Discrete Applied Mathematics 12 (1985) 123–138.
J. Feigenbaum, R. Haddad: On Factorable Extensions and Subgraphs of Prime Graphs, SIAM J. Disc. Math 2 (1989) 197–218.
J.Feigenbaum and A.A.Schäffer: Recognizing composite graphs is equivalent to testing graph isomorphism, SIAM J.Comp. 15 (1986) 619–627.
J.Feigenbaum and A.A.Schäffer: Finding the Prime Factors of Strong Direct Product Graphs in Polynomial Time, Discrete Math. 109 (1992) 77–102.
R.L.Graham and P.M.Winkler: On Isometric Embeddings of Graphs, Transactions of the American Mathematical Society 288 (1985) 527–536.
J. Hagauer, W. Imrich and S. Klavžar: Recognizing graphs of windex 2, Preprint, 1993.
W.Imrich and H.Izbicki: Associative Products of Graphs, Monat. für Math. 80 (1975) 277–281.
W.Imrich and S.Klavžar: A simple O(mn) algorithm for recognizing Hamming graphs, Bull. Inst. Combin. Appl. 9 (1993) 45–56.
W.Imrich and J.Žerovnik: Factoring Cartesian-product Graphs, Journal of Graph Theory 18 (1994) 557–567.
W.Imrich and J.Žerovnik: On the weak reconstruction of Cartesian-product graphs, Discrete Mathematics, vol. 150 (1996) 167–178.
W.Imrich, T.Pisanski and J.Žerovnik, Recognizing Cartesian graph bundles, to appear in Discrete Mathematics.
L.Lovasz: Operations with structures, Acta Math. Acad. Sci. Hungaricae 18 (1967) 321–328.
T.Pisanski, J.Shawe-Taylor and J.Vrabec, Edge-colorability of graph bundles. Journal of Combinatorial Theory Series B 35 (1983) 12–19.
T.Pisanski and J.Vrabec, Graph bundles, unpublished manuscript, 1982.
G.Sabidussi: Graph Multiplication, Mathematische Zeitschrift 72 (1960) 446–457.
V.G.Vizing: The Cartesian Product of Graphs (in Russian), Vyčisl.Syst. 9 (1963) 30–43, (English translation: Comp.El.Syst. 2 (1966) 352–365).
P.M.Winkler: Factoring a Graph in Polynomial Time, European Journal of Combinatorics 8 (1987) 209–212.
J.Žerovnik, A simple algorithm for factoring Cartesian product graphs, Arbeitsbericht 5/1991, Montanuniversitaet Leoben.
J.Hagauer and J.Žerovnik, An algorithm for the weak reconstruction of Cartesian-product graphs, submitted. (also in Preprint Series Vol.33 (1995) 470, Department of Mathematics, University of Ljubljana.)
J.Žerovnik, Recognizing strong bundles, in preparation.
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© 1996 Springer-Verlag Berlin Heidelberg
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Žerovnik, J. (1996). Recognizing graph products and bundles. In: Jeffery, K.G., Král, J., Bartošek, M. (eds) SOFSEM'96: Theory and Practice of Informatics. SOFSEM 1996. Lecture Notes in Computer Science, vol 1175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037431
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DOI: https://doi.org/10.1007/BFb0037431
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