"In 1964, a mathematician named Vadim Vizing proved a shocking result: No matter how large a graph is, it’s easy to figure out how many colors you’ll need to color it. Simply look for the maximum number of lines (or edges) connected to a single point (or vertex), and add 1."
I keep wondering why I ever read Quanta Magazine. It takes a pretty generous reading of "need" to make this a correct statement.
If you read the introduction, you'll also read that the goal is to "color each of your lines and require that for every point, no two lines connected to it have the same color."
Ps. "How many colors a graph needs" is a very well established term in computer science and graph theory.
Personally, I would interpret this as option 1 (and so did the comment above I assume). In that case, the statement is wrong. But I’d prefer to specify „at most/ at least“ anyways.
Or even better, use actual vocabulary. „For every graph there exists a coloring with X colors.“ or „any graph can be coloured using X colors“.
PS: I also agree with the sentiment about quanta magazine. It’s hard to get some actual information from their articles if you know the topic.
No matter how large a car is, it is easy to figure out how much money you'll need to buy it. Simply look at the price tag.
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