Partial Star Products: A Local Covering Approach for the Recognition of Approximate Cartesian Product Graphs
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This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embedding of the graph under investigation into Cartesian product graphs.
Mathematics Subject Classification (2010)Primary 68R10 Secondary 05C85
KeywordsCartesian product Approximate product Partial star product Product relation
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- 3.Feigenbaum, J.: Product graphs: some algorithmic and combinatorial results. Technical Report STAN-CS-86-1121, Stanford University, Computer Science, PhD Thesis (1986)Google Scholar
- 7.Hagauer J., Žerovnik J.: An algorithm for the weak reconstruction of Cartesian-product graphs. J. Combin. Inf. Syst. Sci. 24, 97–103 (1999)Google Scholar
- 8.Hammack R., Imrich W., Klavžar S.: Handbook of Product Graphs. Discrete Mathematics and its Applications 2nd edn. CRC Press, Boca Raton (2011)Google Scholar
- 12.Hellmuth, M., Ostermeier, L., Stadler, P.F.: Unique square property, equitable partitions, and product-like graphs. Discrete Math. (2013, submitted). http://arxiv.org/abs/1301.6898
- 13.Imrich W., Klavžar S.: Product graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York (2000)Google Scholar
- 14.Imrich W., Klavžar S., Rall F.D.: Topics in Graph Theory: Graphs and Their Cartesian Product. AK Peters Ltd., Wellesley (2008)Google Scholar
- 19.Imrich, W., Zmazek, B., Žerovnik, J.: Weak k-reconstruction of Cartesian product graphs. Electron. Notes Discrete Math. 10, 297–300 (2001). Comb01, Euroconference on Combinatorics, Graph Theory and ApplicationsGoogle Scholar