A rigid graph for every set
✍ Scribed by Jaroslav Nešetřil
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 60 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
A graph G is called rigid if the identical mapping V(G)→V(G) is the only homomorphism G→G. In this note we give a simple construction of a rigid oriented graph on every set. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 108–110, 2002
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Let Vbe a set of bit strings of length k, i.e., V C {0, l}'. The query graph Q ( V ) is defined as follows: the vertices of Q(V) are the elements of V, and {O,V} is an edge of Q ( V ) if and only if no other W E Vagrees with U in all the positions in which V does. If Vrepresents the set of keys for
~~r~h-~~lland Publishing Company Receiwd 4 kbrurary 1974 \* ph-them-etic tei7ninolcllgy use in this nste, see [ 21; for alge-; a gxoupoid (i.e., a set with a binary mmposition) in whi rary two eleme the equations 42s = b and 332 =t I ueiy defined s d ~7. Since associative quasigroups are gmups, the