A cancellation property for the direct product of graphs

• Autorzy: Richard H. Hammack
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

graph products; graph direct product; cancellation

Kategorie tematyczne

• 05C60: Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 179-184

Daty

wydano

2008

otrzymano

2007-08-13

poprawiono

2007-12-05

zaakceptowano

2007-12-05

Twórcy

autor

Richard H. Hammack

• Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA

Bibliografia

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

Identyfikatory

DOI

10.7151/dmgt.1400