Regarding the Hadwiger Conjecture

  • Ikorong Annouk
Keywords: true pal, hadwiger index, parent, optimal coloration, uniform graph, relative subgraph, hadwigerian, hadwigerian subgraph, maximal hadwigerian subgraph, hadwiger caliber


The Hadwiger conjecture (see [1] or [2]) is well known. The Hadwiger conjecture states that every graph G satisfies χ(G) ≤ η(G) [where η(G) is the hadwiger number of G (i.e. the maximum of p such that G is contractible to the complete graph Kp), and χ(G) is the chromatic number of G. We recall (see [2]) that the famous four-color problem is a special case of the Hadwiger conjecture]. In this paper, we give the original reformulation of the Hadwiger conjecture and the algebraic reformulation of the Hadwiger conjecture. The algebraic reformulation of the Hadwiger conjecture (which is based on the original reformulation of the Hadwiger conjecture) shows that the proof of this conjecture is strongly linked to a very small class of graphs.


[1] Annouk, I. (2012). Around The Hadwiger Conjecture And The Berge Problem. International Journal of Mathematical Combinatorics, 3, 72 − 82.
[2] Saaty, T. L. & Kainen, P. C. (1986). The Four-Color Problem. Assaults and conquest. New York: Dover Publication, Inc.
How to Cite
Annouk, I. (2024). Regarding the Hadwiger Conjecture. European Journal of Science, Innovation and Technology, 4(1), 393-403. Retrieved from