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Products of graphs pose challenging algebraic,
combinatorial and algorithmic problems. There are difficult open
problems pertaining to the factorization of infinite graphs, the prime
factorization of bipartite finite graphs with respect to the direct
product, and the design of polynomial algorithms for the prime
factorization of directed graphs with respect to the direct product.
Recently new results have been obtained in all these areas.
This talk will focus on a new, short proof for the uniqueness of the
prime factorization of connected graphs with respect to the strong
product and new, fast algorithms for the prime factorization of strong
and direct products.
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