Universal H?colorable Graphs without a given Connguration Aaliated Graduate Student Member 2 Dimacs Reu Participant
نویسندگان
چکیده
For every pair of nite connected graphs F and H, and every integer k, we construct a universal graph U with the following properties: 1. There is a homomorphism : U ! H, but no homomorphism from F to U . 2. For every graph G with maximal degree no more than k having a homomorphism h : G! H, but no homomorphism from F to G, there is a homomorphism : G! U , such that h = . Particularly, this solves a problem presented in [1] and [2] regarding the chromatic number of a universal graph.
منابع مشابه
Reu 2007
Bn : (∀x1, . . . , xn)( if all xi are distinct then the subgraph induced on x1, . . . , xn is 3-colorable). By Erdős-DeBruijn, the countable set of axioms Bn (n = 1, 2, . . . ) defines 3-colorability. To show that 3-colorability is not finitely axiomatizable, we show the (apparently) stronger result that non-3-colorability is not axiomatizable. To do this, we use ultraproducts. It suffices to c...
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