On $b$-continuity of Kneser Graphs of Type $KG(2k+1,k)$

Abstract

In this paper, we introduce a special kind of graph homomorphisms namely semi-locally-surjective graph homomorphisms. We show some relations between semi-locally-surjective graph homomorphisms and colorful colorings of graphs. Then, we prove that for each natural number $k$, the Kneser graph KG$(2k+1,k)$ is $b$-continuous. Finally, we present some special conditions for graphs to be $b$continuous.