Cancellation of direct products of digraphs

Richard H. Hammack; Katherine E. Toman

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 4, page 575-590
  • ISSN: 2083-5892

Abstract

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We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.

How to cite

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Richard H. Hammack, and Katherine E. Toman. "Cancellation of direct products of digraphs." Discussiones Mathematicae Graph Theory 30.4 (2010): 575-590. <http://eudml.org/doc/271052>.

@article{RichardH2010,
abstract = {We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.},
author = {Richard H. Hammack, Katherine E. Toman},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph direct product; graph product cancellation; digraphs},
language = {eng},
number = {4},
pages = {575-590},
title = {Cancellation of direct products of digraphs},
url = {http://eudml.org/doc/271052},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Richard H. Hammack
AU - Katherine E. Toman
TI - Cancellation of direct products of digraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 4
SP - 575
EP - 590
AB - We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.
LA - eng
KW - graph direct product; graph product cancellation; digraphs
UR - http://eudml.org/doc/271052
ER -

References

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  1. [1] R. Hammack, A cancellation property for the direct product of graphs, Discuss. Math. Graph Theory 28 (2008) 179-185, doi: 10.7151/dmgt.1400. Zbl1154.05045
  2. [2] R. Hammack, On direct product cancellation of graphs, Discrete Math. 309 (2009) 2538-2543, doi: 10.1016/j.disc.2008.06.004. Zbl1210.05124
  3. [3] P. Hell and J. Nesetril, Graphs and Homomorphisms, Oxford Lecture Series in Mathematics (Oxford U. Press, 2004), doi: 10.1093/acprof:oso/9780198528173.001.0001. Zbl1062.05139
  4. [4] W. Imrich and S. Klavžar, Product Graphs: Structure and recognition, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley and Sons, New York, 2000). 
  5. [5] L. Lovász, On the cancellation law among finite relational structures, Period. Math. Hungar. 1 (1971) 145-156, doi: 10.1007/BF02029172. Zbl0223.08002

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