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

Wilfried Imrich; Werner Klöckl

Discussiones Mathematicae Graph Theory (2007)

  • Volume: 27, Issue: 3, page 593-601
  • ISSN: 2083-5892

Abstract

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By a result of McKenzie [4] finite directed graphs that satisfy certain connectivity and thinness conditions have the unique prime factorization property with respect to the cardinal product. We show that this property still holds under weaker connectivity and stronger thinness conditions. Furthermore, for such graphs the factorization can be determined in polynomial time.

How to cite

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Wilfried Imrich, and Werner Klöckl. "Factoring directed graphs with respect to the cardinal product in polynomial time." Discussiones Mathematicae Graph Theory 27.3 (2007): 593-601. <http://eudml.org/doc/270411>.

@article{WilfriedImrich2007,
abstract = {By a result of McKenzie [4] finite directed graphs that satisfy certain connectivity and thinness conditions have the unique prime factorization property with respect to the cardinal product. We show that this property still holds under weaker connectivity and stronger thinness conditions. Furthermore, for such graphs the factorization can be determined in polynomial time.},
author = {Wilfried Imrich, Werner Klöckl},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {directed graphs; cardinal product; graph algorithms},
language = {eng},
number = {3},
pages = {593-601},
title = {Factoring directed graphs with respect to the cardinal product in polynomial time},
url = {http://eudml.org/doc/270411},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Wilfried Imrich
AU - Werner Klöckl
TI - Factoring directed graphs with respect to the cardinal product in polynomial time
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 3
SP - 593
EP - 601
AB - By a result of McKenzie [4] finite directed graphs that satisfy certain connectivity and thinness conditions have the unique prime factorization property with respect to the cardinal product. We show that this property still holds under weaker connectivity and stronger thinness conditions. Furthermore, for such graphs the factorization can be determined in polynomial time.
LA - eng
KW - directed graphs; cardinal product; graph algorithms
UR - http://eudml.org/doc/270411
ER -

References

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  1. [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. Zbl0786.68076
  2. [2] W. Imrich, Factoring cardinal product graphs in polynomial time, Discrete Math. 192 (1998) 119-144, doi: 10.1016/S0012-365X(98)00069-7. Zbl0955.68089
  3. [3] 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. 
  4. [4] R. McKenzie, Cardinal multiplication of structures with a reflexive relation, Fund. Math. 70 (1971) 59-101. Zbl0228.08002

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