The oriented chromatic number o(H) of an oriented graph H is de ned as the minimum order of an oriented graph H ′ such that H has a homomorphism to H ′. The oriented chromatic number o(G) of an undirected graph G is then de ned as the maximum oriented chromatic number of its orientations. In this paper we study the links between o(G) and mad(G) de ned as the maximum average degree of the subgra...

The clique number of an undirected graphG is the maximum order of a complete subgraph of G and is a well-known lower bound for the chromatic number ofG. Every proper k-coloring of G may be viewed as a homomorphism (an edge-preserving vertex mapping) of G to the complete graph of order k. By considering homomorphisms of oriented graphs (digraphs without cycles of length at most 2), we get a natu...

In this paper we consider an oriented version of adjacency graphs of triangulations of bordered surfaces with marked points. We develop an algorithm that determines whether a given oriented graph is an oriented adjacency graph of a triangulation. If a given oriented graph corresponds to many triangulations, our algorithm finds all of them. As a corollary we find out that there are only finitely...

The oriented chromatic number χo(~ G) of an oriented graph ~ G = (V,A) is the minimum number of vertices in an oriented graph ~ H for which there exists a homomorphism of ~ G to ~ H. The oriented chromatic number χo(G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the orientations of G. This paper discusses the relation between the oriented chromatic number an...

Abstract Attributed graph embedding aims to learn node representation based on the topology and attributes. The current mainstream GNN-based methods of target by aggregating attributes its neighbor nodes. These still face two challenges: (1) In neighborhood aggregation procedure, each would be propagated neighborhoods which may cause disturbance original over-smoothing in GNN iteration. (2) Bec...