Suppose G and H are graphs. We say G is H-colorable if there is a homomorphism (edge-preserving vertex mapping) from G to H. We say a graph G is uniquely H-colorable if there is an onto homomorphism c from G to H, and any other homomorphism from G to H is the composition o o c of c with an automorph
Construction of uniquelyH-colorable graphs
โ Scribed by Zhu, Xuding
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 190 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
We shall prove that for any graph H that is a core, if ฯ(G) is large enough, then H ร G is uniquely H-colorable. We also give a new construction of triangle free graphs, which are uniquely n-colorable.
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