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

TL;DR

This paper introduces semi-locally-surjective graph homomorphisms, explores their relation to colorful colorings, and proves that Kneser graphs of the form KG(2k+1,k) are b-continuous, also identifying conditions for b-continuity.

Contribution

It defines semi-locally-surjective homomorphisms, links them to colorful colorings, and proves the b-continuity of KG(2k+1,k) graphs, advancing understanding of graph homomorphism properties.

Findings

KG(2k+1,k) are b-continuous for all natural k

Introduces semi-locally-surjective homomorphisms and relates them to colorful colorings

Provides conditions under which graphs are b-continuous

Abstract

In this paper, we will introduce an special kind of graph homomorphisms namely semi-locally-surjective graph homomorphisms and show some relations between semi-locally-surjective graph homomorphisms and colorful colorings of graphs 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 conditions for graphs to be $b$-continuous.