The Rooted Tree Embedding Problem into Points in the Plane.
The structure of plane graphs with independent crossings and its applications to coloring problems
If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity of G is...
The tau constant of a metrized graph and its behavior under graph operations.
Toughness of -minor-free graphs.
Towards the Albertson conjecture.
Transitions in Geometric Minimum Spanning Trees.
Transitive planar graphs
Triangle Decompositions of Planar Graphs
A multigraph G is triangle decomposable if its edge set can be partitioned into subsets, each of which induces a triangle of G, and rationally triangle decomposable if its triangles can be assigned rational weights such that for each edge e of G, the sum of the weights of the triangles that contain e equals 1. We present a necessary and sufficient condition for a planar multigraph to be triangle decomposable. We also show that if a simple planar graph is rationally triangle decomposable, then it...
Triangle-free planar graphs with minimum degree 3 have radius at least 3
We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.
Triangulations and the Hajós conjecture.
Triples, current graphs and biembeddings.
Two new classes of trees embeddable into hypercubes
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube and its use in several domains, such as: the coding theory, transfer of information, multicriteria rule,...
Two new classes of trees embeddable into hypercubes
The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube and its use in several domains, such as: the coding theory, transfer of information, multicriteria rule,...
Two-fold branched coverings of S3 have type six.
In this work, we prove that every closed, orientable 3-manifold M3 which is a two-fold covering of S3 branched over a link, has type six.
Two-layer planarization: improving on parameterized algorithmics.