The Kontsevich graph orientation morphism revisited

Graph Cohomology and Kontsevich Cycles

We use the duality between compactly supported cohomology of the associative graph complex and the cohomology of the mapping class group to show that the duals of the Kontsevich cycles [Wλ] correspond to polynomials in the Miller-Morita-Mumford classes. We also compute the coefficients of the first two terms of this polynomial. This extends the results of [Igu], giving a more detailed answer to...

The random graph revisited

The random graph, or Rado’s graph (the unique countable homogeneous graph) has made an appearance in many parts of mathematics since its first occurrences in the early 1960s. In this paper I will discuss some old and new results on this remarkable structure.

The Gray graph revisited

Certain graph theoretic properties and alternative de nitions of the Gray graph the smallest known cubic edge but not vertex transitive graph are discussed in detail Introduction history The smallest known cubic edge but not vertex transitive graph has vertices and is known as the Gray graph denoted hereafter by G The rst published account on the Gray graph is due to Bouwer who mentioned that t...

The Random Graph Revisited

Orientation distance graphs revisited

The orientation distance graph Do(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to ex...