TROTIGNON , Nicolas

A wheel is a graph formed by a chordless cycle and a vertex that has at least three neighbors in the cycle. We prove that every 3-connected graph that does not contain a wheel as a subgraph is in fact minimally 3-connected. We prove that every graph that does not contain a wheel as a subgraph is 3-colorable.

We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) $G$, does it contain an induced subdivision of a prescribed digraph $D$? The complexity of this problem depends on $D$ and on whether $H$ must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial...

We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) G, does it contain an induced subdivision of a prescribed digraph D? The complexity of this problem depends on D and on whether G must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial...

We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) H, does it contain an induced subdivision of a prescribed digraph D? The complexity of this problem depends on D and on whether H is an oriented graph or contains 2-cycles. We announce a number of examples of polynomial instances as well as...

A graph G has maximal local edge-connectivity k if the maximum number of edge-disjoint paths between every pair of distinct vertices x and y is at most k. We prove Brooks-type theorems for k-connected graphs with maximal local edge-connectivity k, and for any graph with maximal local edge-connectivity 3. We also consider several related graph...