Alejandro Erickson

Research Associate
School of Engineering and Computing Sciences, Durham University
United Kingdom

“Five 2-Colourings of the Petersen Graph” is a watercolour and acrylic india ink study of my favourite drawings of the Petersen graph in 2 colours, Cadmium Yellow and Ultramarine Blue, and their shades.

In spite of the Petersen graph's small size, its structure is beautifully symmetric and it has far-reaching consequences. Whole books have been written about it.

Indeed I provide no proper 2-colouring of the Petersen graph in the mathematical sense, as this is impossible. Instead I use colour to counter the often rigid interpretation of these images and highlight some features of the drawings which may not, at first, be noticed. This symbolizes how breakthroughs in mathematics are most often born of creativity.

Five 2-Colourings of the Petersen Graph
Five 2-Colourings of the Petersen Graph
59cm x 60cm
water colour paint, acrylic india ink, digital print

“You just want to give the impression of bushes,” said my painting instructor.

What is an “impression” of the Petersen graph? The tension between art and mathematical concepts often sets artistic expression against details, similar to my instructor’s bushes. A “mathematical impressionism” emerges in which the scene is a mathematical concept, and the impressionist delivers their artistic representation of it.

I challenged myself to explicitly highlight several mathematical concepts in “Five 2-Colourings of the Petersen Graph”, and to give a tastefully didactic impression of this champion of discrete mathematics.