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Vertex colouring, Edge Colouring, List Colouring, Fractional Chromatic Number and other variants of graph colouring problems are all on topic.

35 votes
Accepted

Can we three-color a tiling of the plane with Smith, Meyers, Kaplan, and Goodman-Strauss's e...

No, you cannot three-color that tiling. Here's a finite part of the tiling from page 10 top left of the article, the tile numbered 2 here is the one darkened on that figure. This part cannot be three- …
Zsbán Ambrus's user avatar
8 votes
2 answers
657 views

Fractional chromatic number, find reference to a particular alternate definition for

I'm searching for a reference to a particular alternate definition of the fractional chromatic number of graphs. Let me review the most common definition and basic properties first. Let $ G $ be …
Zsbán Ambrus's user avatar
2 votes

Fractional chromatic number, find reference to a particular alternate definition for

Wilfried Imrich, Sandi Klavžar, Product Graphs, Structure and Recognition gives this as theorem 8.38 on page 268 as well. I should have looked in this book earlier, but now Dan Stahlke's answer made …
Zsbán Ambrus's user avatar