We present a framework for embedding graph structured data into vector space, taking account node features and structures of graphs the optimal transport (OT) problem. Then we propose novel distance between two graphs, named LinearFGW, defined as Euclidean their embeddings. The advantages proposed are twofold: 1) it takes measuring dissimilarity in kernel-based framework, 2) is more efficient c...

A Meyniel obstruction is an odd cycle with at most one chord and a graph is Meyniel if and only if it has no Meyniel obstruction. The authors have found in a previous work a linear-time algorithm for optimaly color the vertices of a Meyniel graph. Here we extend this algorithm to obtain a linear-time algorithm that, for any graph, colors optimally the vertices of the graph or finds a Meyniel ob...

The class of distance hereditary graphs consists of the isometric graphs. That is, for each pair of vertices, its distance is invariant for any induced path in a distance hereditary graph. In the paper, a canonical tree representation of a distance hereditary graph is proposed. A linear time algorithm for computing the tree representation is also presented. Hence the recognition problem and the...

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in R.

This paper deals with verification of timed and untimed linear properties of the Interval Timed Colored Petri Net model. This model can simulate other timed colored Petri nets and allows describing large and complex real-time systems. We propose here to contract its generally infinite state space into a graph that captures all linear properties of the model. The resulting graph is finite iff, t...

A linear colouring of a graph is a proper vertex colouring such that the subgraph induced by any two colour classes is a set of vertex disjoint paths. The corresponding linear chromatic number of a graph G, namely lc(G), is the minimum number of colours in a linear colouring of G. We prove that for a graph G with girth g ≥ 8 and maximum degree ∆ ≥ 7 the inequality on its linear colouring number...