My math sibling Anton Dochtermann recently posted a paper to the Arxiv, HOM COMPLEXES AND HOMOTOPY THEORY IN THE CATEGORY OF GRAPHS introducing the idea of weak equivalence to the category of graphs (model graph category anyone?) and subsumes other graph homotopy theories into the framework. This is all a natural progression of research that has its roots in in the topological ideas introduced in Lov’asz’s proof of Kneser’s conjecture and culminates in K-theory for graphs I suppose.

Stay tuned for a paper from another math sibling Matt Kahle, giving classes of graphs for which the chromatic number estimate in Lov’asz’s proof is tight.