# A cancellation property for the direct product of graphs

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 1, page 179-184
- ISSN: 2083-5892

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topRichard H. Hammack. "A cancellation property for the direct product of graphs." Discussiones Mathematicae Graph Theory 28.1 (2008): 179-184. <http://eudml.org/doc/270517>.

@article{RichardH2008,

abstract = {Given graphs A, B and C for which A×C ≅ B×C, it is not generally true that A ≅ B. However, it is known that A×C ≅ B×C implies A ≅ B provided that C is non-bipartite, or that there are homomorphisms from A and B to C. This note proves an additional cancellation property. We show that if B and C are bipartite, then A×C ≅ B×C implies A ≅ B if and only if no component of B admits an involution that interchanges its partite sets.},

author = {Richard H. Hammack},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph products; graph direct product; cancellation},

language = {eng},

number = {1},

pages = {179-184},

title = {A cancellation property for the direct product of graphs},

url = {http://eudml.org/doc/270517},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Richard H. Hammack

TI - A cancellation property for the direct product of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 1

SP - 179

EP - 184

AB - Given graphs A, B and C for which A×C ≅ B×C, it is not generally true that A ≅ B. However, it is known that A×C ≅ B×C implies A ≅ B provided that C is non-bipartite, or that there are homomorphisms from A and B to C. This note proves an additional cancellation property. We show that if B and C are bipartite, then A×C ≅ B×C implies A ≅ B if and only if no component of B admits an involution that interchanges its partite sets.

LA - eng

KW - graph products; graph direct product; cancellation

UR - http://eudml.org/doc/270517

ER -

## References

top- [1] R. Hammack, A quasi cancellation property for the direct product, Proceedings of the Sixth Slovenian International Conference on Graph Theory, under review. Zbl1154.05045
- [2] 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
- [3] W. Imrich and S. Klavžar, Product Graphs; Structure and Recognition (Wiley Interscience Series in Discrete Mathematics and Optimization, 2000). Zbl0963.05002
- [4] L. Lovász, On the cancellation law among finite relational structures, Period. Math. Hungar. 1 (1971) 59-101.

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