Saeed Shaebani

Assistant Professor of Pure Mathematics

Selected Publications

Shaebani, S. A note on color chains of graphs (2018) Ars Combinatoria, 141, pp. 313-317. 

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.

AUTHOR KEYWORDS: Achromatic number; B-chromatic number; Chromatic number; Fall achromatic number; Fall chromatic number; Grundy chromatic number; Partial grundy chromatic number
PUBLISHER: Charles Babbage Research Centre

Shaebani, S. A note on b-coloring of Kneser graphs (2018) Discrete Applied Mathematics, . Article in Press.

DOI: 10.1016/j.dam.2018.09.013

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.

AUTHOR KEYWORDS: b-chromatic number; b-coloring; Kneser graph
INDEX KEYWORDS: Combinatorial mathematics, B-chromatic number; Kneser graph; Upper Bound, Mathematical techniques
PUBLISHER: Elsevier B.V.