5-choosability of graphs with crossings far apart

We give a new proof of the fact that every planar graph is 5-choosable, and use it to show that every graph drawn in the plane so that the distance between every pair of crossings is at least 15 is 5-choosable. At the same time we may allow some vertices to have lists of size four only, as long as they are far apart and far from the crossings.Comment: 55 pages, 11 figures; minor revision according to the referee suggestion

Every longest circuit of a 3-connected, K3,3K_{3,3}-minor free graph has a chord

Carsten Thomassen conjectured that every longest circuit in a 3-connected graph has a chord. We prove the conjecture for graphs having no $K_{3,3}$ minor, and consequently for planar graphs.Comment: accepted by Journal of Graph Theor

The square of a planar cubic graph is 77-colorable

We prove the conjecture made by G.Wegner in 1977 that the square of every planar, cubic graph is $7$-colorable. Here, $7$ cannot be replaced by $6$

A generalised nested-logit model of the demand for automobile variants

This paper estimates the demand for car model variants instead of looking only at demand for models in terms of the ’baseline’ variant of each model as done in the literature. The data has sex and age of the buyer for every car sold in Norway 2000-2004, in addition to characteristics of the cars. The demand model uses this information to estimate taste coefficients which depend on demographic characteristics. A nested logit model and a generalised nested logit model are used to induce correlation in the logit error between products with observable and unobservable similarities. Results indicate that it may be problematic to have different logit errors for every product when the number of products is very high, even when allowing for flexible correlation patterns.

Automobile engine variants and price discrimination

Using a structural model of demand for automobile engine variants, this paper finds that there is second-degree price discrimination: markups increase with engine size. Still, average markups are lower than when models have just one engine. The paper develops the first empirical demand framework suitable for markets with variants. There is an unobserved product characteristic and a consumer-specific logit term for classes of products, but both are fixed across variants. Fixed effects control for unobservables. The literature’s assumption of orthogonality between unobserved and observed product characteristics is not needed.second-degree price discrimination, automobiles, discrete-choice demand models