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In this paper, we will introduce an special kind of graph homomorphismsnamely semi-locally-surjective graph homomorphisms and show some relationsbetween semi-locally-surjective graph homomorphisms and colorful colorings ofgraphs and then we prove that for each natural number $k$, the Kneser graph$KG(2k+1,k)$ is $b$-continuous. Finally, we introduce some special conditionsfor graphs to be $b$-continuous.

On b-continuity Of Kneser Graphs of type KG(2k+1,k)