Sequentially embeddable graphs

On cyclically embeddable graphs

An embedding of a simple graph G into its complement G is a permutation σ on V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.

Clin d’oeil on Lj-embeddable planar graphs

In this note we present some properties of LI-embeddable planar graphs. We present a characterization of graphs isometrically embeddable into half-cubes. This result implies that every planar Li-graph G has a scale 2 embedding into a hypercube. Further, under some additional conditions we show that for a simple circuit C of a planar Li-graph G the subgraph H of G bounded by C is also Li-embedda...

Sequentially Cohen-Macaulay Graphs of Form θ_{n1, ...nk}

On cyclically embeddable (n, n-1)-graphs

An embedding of a simple graph G into its complement G is a permutation σ on V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n, n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.

Vertex Splitting and Upper Embeddable Graphs

The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak minor of G is also in G. Up to now, there are few results providing the necessary and sufficient conditions for characterizing upper embeddability of graphs...