Factoring directed graphs with respect to the cardinal product in polynomial time II

• Autorzy: Wilfried Imrich , Werner Klöckl
• Języki publikacji: EN

Abstrakty

EN

By a result of McKenzie [7] all finite directed graphs that satisfy certain connectivity conditions have unique prime factorizations with respect to the cardinal product. McKenzie does not provide an algorithm, and even up to now no polynomial algorithm that factors all graphs satisfying McKenzie's conditions is known. Only partial results [1,3,5] have been published, all of which depend on certain thinness conditions of the graphs to be factored.
In this paper we weaken the thinness conditions and thus significantly extend the class of graphs for which the prime factorization can be found in polynomial time.

Słowa kluczowe

EN

directed graphs; cardinal product; graph algorithms

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments
• 05C75: Structural characterization of families of graphs
• 05C85: Graph algorithms
• 05C76: Graph operations (line graphs, products, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 3
• Strony: 461-474

Daty

wydano

2010

otrzymano

2009-07-16

poprawiono

2009-10-07

zaakceptowano

2009-10-12

Twórcy

autor

Wilfried Imrich

• Chair of Applied Mathematics, Montanuniversität, 8700 Leoben, Austria

autor

Werner Klöckl

• Chair of Applied Mathematics, Montanuniversität, 8700 Leoben, Austria

Bibliografia

• [1] J. Feigenbaum and A.A. Schäffer, Finding the prime factors of strong direct product graphs in polynomial time, Discrete Math. 109 (1992) 77-102, doi: 10.1016/0012-365X(92)90280-S.
• [2] M. Hellmuth, W. Imrich, W. Klöckl and P. Stadler, Approximate graph products, Europ. J. Combinatorics 30 (2009) 1119-1133, doi: 10.1016/j.ejc.2008.09.006.
• [3] W. Imrich, Factoring cardinal product graphs in polynomial time, Discrete Math. 192 (1998) 119-144, doi: 10.1016/S0012-365X(98)00069-7.
• [4] W. Imrich and S. Klavžar, Product graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization (Wiley-Interscience, New York, 2000), Structure and recognition, With a foreword by Peter Winkler.
• [5] W. Imrich and W. Klöckl, Factoring directed graphs with respect to the cardinal product in polynomial time, Discuss. Math. Graph Theory 27 (2007) 593-601, doi: 10.7151/dmgt.1385.
• [6] W. Klöckl, On the cardinal product, Ph.D. thesis (Montanuniversität Leoben, Austria, 2007).
• [7] R. McKenzie, Cardinal multiplication of structures with a reflexive relation, Fund. Math. 70 (1971) 59-101.

Identyfikatory

DOI

10.7151/dmgt.1507