Abstract
We relate acyclic (and star) chromatic number of a graph to the chromatic number of its minors and as a consequence we show that the set of all triangle free planar graphs is homomorphism bounded by a triangle free graph. This solves a problem posed in [[15]]. It also improves the best known bound for the star chromatic number of planar graphs from 80 to 30. Our method generalizes to all minor closed classes and puts Hadwiger conjecture in yet another context.
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