Stable Kneser Graphs are almost all not weakly Hom-Idempotent

Abstract : A graph G is said to be hom-idempotent if there is an homomorphism from G 2 to G, and weakly hom-idempotent if for some n ≥ 1 there is a homomorphism from G n+1 to G n . Larose et al. [Eur. J. Comb. 19:867-881, 1998] proved that Kneser graphs KG(n, k) are not weakly hom-idempotent for n ≥ 2k + 1, k ≥ 2. We show that 2-stable Kneser graphs KG(n, k) 2−stab are not weakly hom-idempotent, for n ≥ 2k + 2, k ≥ 2. Moreover, for s, k ≥ 2, we prove that s-stable Kneser graphs KG(ks+1, k) s−stab are circulant graphs and so hom-idempotent graphs.
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Pablo Torres, Mario Valencia-Pabon. Stable Kneser Graphs are almost all not weakly Hom-Idempotent . 2015. ⟨hal-01119741⟩

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