A Weak form of Hadwiger's Conjecture

Dominic van der Zypen

doi:10.6000/1927-5129.2014.10.23

A Weak form of Hadwiger's Conjecture

Authors

Dominic van der Zypen M&S Software Engineering, Morgenstrasse 129, CH-3018 Bern, Switzerland

DOI:

https://doi.org/10.6000/1927-5129.2014.10.23

Keywords:

Graph theory, graph colouring, graph minors, Hadwiger's conjecture

Abstract

We introduce the following weak version of Hadwiger's conjecture: If G is a graph and is a cardinal such that there is no coloring map c:G, then K is a minor of G. We prove that this statement is true for graphs with infinite chromatic number.

References

Robertson N, Paul SD, Thomas R, Excluding subdivisions of infinite cliques. Trans Am Math Soc 1992; 332(1): 211-23.

Hugo Hadwiger, ber eine Klassifikation der Streckenkomplexe. Vierteljschr Naturforsch Ges Zrich 1943; 88: 133-43.

Dominic van der Zypen, Hadwiger's conjecture for graphs with infinite chromatic number. Advancement and Development in Mathematical Sciences 2013; 4(1&2): 1-4.

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Published

2014-01-05

How to Cite

Dominic van der Zypen. (2014). A Weak form of Hadwiger’s Conjecture. Journal of Basic & Applied Sciences, 10, 170–172. https://doi.org/10.6000/1927-5129.2014.10.23

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Issue

Vol. 10 (2014)

Section

Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.