An Infinite Family of Linklessly Embeddable Tutte-4-Connected Graphs

Distributed Approximation Algorithms for k-dominating Set in Graphs of Bounded Genus and Linklessly Embeddable Graphs

A k-dominating set in a graph G = (V,E) is a set U ⊆ V such that ever vertex of G is either in U or has at least k neighbors in U . In this paper we give simple distributed approximation algorithms in the local model for the minimum k-dominating set problem for k ≥ 2 in graphs with no K3,h-minor and graphs with no K4,4-minor. In particular, this gives fast distributed approximations for graphs ...

An infinite Family of Non-embeddable Hadamard Designs

The parameters 2 (2λ + 2, λ + 1, λ) are those of a residual Hadamard 2 (4λ + 3, 2λ + 1, λ) design. All 2 (2λ + 2, λ + 1, λ) designs with λ ≤ 4 are embeddable. The existence of non-embeddable Hadamard 2-designs has been determined for the cases λ = 5, λ = 6, and λ = 7. In this paper the existence of an infinite family of non-embeddable 2 (2λ + 2, λ + 1, λ) designs, λ = 3(2m)− 1,m ≥ 1 is establis...

Matroid and Tutte-connectivity in Infinite Graphs

We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same connectivity function. As an application we re-prove that, also for infinite graphs, Tutte-connectivity is invariant under taking dual graphs.

A Borsuk theorem for antipodal links and a spectral characterization of linklessly embeddable graphs

For any undirected graph G, let μ(G) be the graph parameter introduced by Colin de Verdière. In this paper we show that μ(G) ≤ 4 if and only if G is linklessly embeddable (in R). This forms a spectral characterization of linklessly embeddable graphs, and was conjectured by Robertson, Seymour, and Thomas. A key ingredient is a Borsuk-type theorem on the existence of a pair of antipodal linked (k...

Tutte Polynomials of Flower Graphs