A History of Mathematics in South Africa: Modern Milestones
- The Mathematical Intelligencer
Hadwiger Numbers and Gallai-Ramsey Numbers of Special Graphs
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
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.
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
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.
TOWARDS STEINBERG'S CONJECTURE
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…
SHOWING 1-6 OF 6 REFERENCES
Ericas in Southern Africa
- Environmental Science
Ericas in Southern Africa , Ericas in Southern Africa , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
9. Note on the Colouring of Maps
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…
Four Colors Suffice: How the Map Problem Was Solved
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…