We show that f (x) = âŒŠ 2 xâŒ‹ is a Î¸-bounding function for the class of subcubic graphs and that it is best possible. This generalizes a result by Henning et al. (2012), who showed that Î¸ (G) â‰¤ 2Î±(G)â€¦ (More)

The purpose of these notes is to give a substantially self-contained introduction to the factorization of polynomials over number fields. In particular, we present Zassenhausâ€™ algorithm and aâ€¦ (More)

We study the VC-dimension of the set system on the vertex set of some graph which is induced by the family of its k-connected subgraphs. In particular, we give tight upper and lower bounds for theâ€¦ (More)

Definition 1. Let k be a field. An algebraic variety over k is a k-scheme X such that there exists a covering by a finite number of affine open subschemes Xi which are affine varieties over k, i.e.â€¦ (More)

Line graphs constitute a rich and well-studied class of graphs. In this paper, we focus on three different topics related to line graphs of subcubic triangle-free graphs. First, we show that any suchâ€¦ (More)