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Tag Archives: Petersen graph
Aliens Do Exist
The people from the planet Ade have intercepted radio transmissions from Earth, and have discovered that we know about the Petersen graph and the root system E6. One day, a flying saucer from Ade arrives on Earth and delivers an … Continue reading
Posted in doing mathematics, events
Tagged Petersen graph, random graph, root systems, Sira Gratz, University of Leeds
1 Comment
A small fact about the Petersen graph
The Petersen graph has 10 vertices and 15 edges, and the complete graph on 10 vertices has 45 edges. However, Allen Schwenk and (independently) O. P. Lossers (Jack van Lint’s problemsolving seminar in Eindhoven) showed that you can’t partition the … Continue reading
A puzzle for you
The Petersen graph is perhaps the most famous graph of all. It has ten vertices, fifteen edges, valency 3, and no triangles. Since the complete graph on ten vertices has 45 edges and valency 9, one might ask whether the … Continue reading
Counting colourings of graphs
Every graph theorist knows that the colourings of a graph with a given number of colourings are counted by a certain polynomial, the chromatic polynomial of the graph. My purpose here is to point out that there is more to … Continue reading
Posted in exposition, open problems
Tagged acyclic orientations, InclusionExclusion, orbitcounting lemma, Petersen graph
1 Comment