Saeed Shaebani

In [3], Dunbar, et al. asked for the existence of a fall-colorable graph G satisfying the chain of inequalities χ(C) < χf(G) < φf(G) < φ(G) < ∂Γ(G) < φ(G). Balakrishnan and Kavaskar [1] gave an affirmative answer to this question. In this note, we investigate a strengthened form of the question and show that the minimum of differences of consecutive terms in the chain can be arbitrarily large. © 2018 Charles Babbage Research Centre. All Rights Reserved.

In this short note, the purpose is to provide an upper bound for the b-chromatic number of Kneser graphs. Our bound improves the upper bound that was presented by Balakrishnan and Kavaskar (2012). © 2018 Elsevier B.V.