# A note on uniquely H-colourable graphs

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 39-44
- ISSN: 2083-5892

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topAnthony Bonato. "A note on uniquely H-colourable graphs." Discussiones Mathematicae Graph Theory 27.1 (2007): 39-44. <http://eudml.org/doc/270404>.

@article{AnthonyBonato2007,

abstract = {For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.},

author = {Anthony Bonato},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph homomorphisms; core graphs; uniquely H-colourable},

language = {eng},

number = {1},

pages = {39-44},

title = {A note on uniquely H-colourable graphs},

url = {http://eudml.org/doc/270404},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Anthony Bonato

TI - A note on uniquely H-colourable graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 39

EP - 44

AB - For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.

LA - eng

KW - graph homomorphisms; core graphs; uniquely H-colourable

UR - http://eudml.org/doc/270404

ER -

## References

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- [8] J. Kratochvíl, P. Mihók and G. Semanišin, Graphs maximal with respect to hom-properties, Discuss. Math. Graph Theory 17 (1997) 77-88, doi: 10.7151/dmgt.1040. Zbl0905.05038
- [9] X. Zhu, Uniquely H-colorable graphs with large girth, J. Graph Theory 23 (1996) 33-41, doi: 10.1002/(SICI)1097-0118(199609)23:1<33::AID-JGT3>3.0.CO;2-L Zbl0864.05037
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