## 7 Citations

Hadwiger Numbers and Gallai-Ramsey Numbers of Special Graphs

- Mathematics
- 2019

This dissertation explores two separate topics on graphs. We first study a far-reaching generalization of the Four Color Theorem. Given a graph G, we use χ(G) to denote the chromatic number; α(G) the…

Some Fundamental Theorems in Mathematics

- Mathematics
- 2018

An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 135 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful…

Vertex-Coloring with Defects

- MathematicsJ. Graph Algorithms Appl.
- 2017

It is proved that the (edge, 3)-coloring problem remains NP-complete even for graphs with maximum vertex-degree 6, hence answering an open question posed by Cowen et al.

Vertex-Coloring with Star-Defects

- MathematicsWALCOM
- 2016

This paper focuses on defective colorings in which the monochromatic components are acyclic and have small diameter, namely, they form stars, and gives a linear-time algorithm to decide if such a defective coloring exists with two colors and to construct one.

Coloring graphs using topology

- MathematicsArXiv
- 2014

The method is expected to give a reason "why 4 colours suffice" and suggests that every two dimensional geometric graph of arbitrary degree and orientation can be coloured by 5 colours.

TOWARDS STEINBERG'S CONJECTURE

- Mathematics
- 2014

Several conjectures concerning planar graph colorings are still unsolved to this day. One of the more famous ones is Steinberg’s Conjecture (first stated in 1976), which we work towards in this…

## References

SHOWING 1-6 OF 6 REFERENCES

Four colors suffice!

- MathematicsSIGA
- 2005

This column is a review of the recent book "Four colors suffice" by Robin Wilson that might interest the readers of this column since its almost three decades since the result was proven by Appel and Haken.

Four Colors Suffice: How the Map Problem Was Solved

- History
- 2002

On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound…

Ericas in Southern Africa

- Environmental Science
- 1967

Ericas in Southern Africa , Ericas in Southern Africa , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

9. Note on the Colouring of Maps

- History
- 1880

From the Proceedings of the Royal Society of Edinburgh, No. 106, p. 501, it appears the colouring of maps is receiving attention. This note bears chiefly upon the history of the matter. Some thirty…