Add to ORKGWe describe some metric properties of incomparability graphs. We consider the problem of the existence of infinite paths, either induced or isometric, in the incomparability graph of a poset. Among other things, we show that if the incomparability graph of a poset is connected and has infinite diameter, then it contains an infinite induced path. Furthermore, if the diameter of the set of vertices of degree at least $3$ is infinite, then the graph contains as an induced subgraph either a comb or a kite
For an undirected graph G¿=¿(V,E), we say that for l,u,v¿¿¿V, l separates u from v if the distance b...
A class of countable infinite graphs with unbounded vertex degree is con-sidered. In these graphs, t...
Given an input undirected graph G=(V,E), we say that a vertex l separates u from v (where u,v ¿ V) i...
We describe some metric properties of incomparability graphs. We consider the problem of the existen...
Abstract. A set of vertices S resolves a graph G if every vertex is uniquely deter-mined by its vect...
AbstractA set of vertices S resolves a graph G if every vertex is uniquely determined by its vector ...
A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vecto...
AbstractA parity graph is a graph in which any two induced paths joining the same pair of vertices h...
Abstract. We introduce a new class of countably infinite random geometric graphs, whose vertices V a...
AbstractA graph G is traceable if there is a path passing through all the vertices of G. It is prove...
International audienceA set S of isometric paths of a graph G is "v-rooted", where v is a vertex of ...
A graph is k-indivisible, where k is a positive integer, if the deletion of any finite set of vertic...
AbstractThe paper is concerned with certain kinds of random processes in infinite graphs. A finite t...
summary:Let $G$ be a (finite undirected) connected graph (with no loop or multiple edge). The set $\...
In recent years, considerable advances have been made in the study of properties of metric spaces in...
For an undirected graph G¿=¿(V,E), we say that for l,u,v¿¿¿V, l separates u from v if the distance b...
A class of countable infinite graphs with unbounded vertex degree is con-sidered. In these graphs, t...
Given an input undirected graph G=(V,E), we say that a vertex l separates u from v (where u,v ¿ V) i...
We describe some metric properties of incomparability graphs. We consider the problem of the existen...
Abstract. A set of vertices S resolves a graph G if every vertex is uniquely deter-mined by its vect...
AbstractA set of vertices S resolves a graph G if every vertex is uniquely determined by its vector ...
A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vecto...
AbstractA parity graph is a graph in which any two induced paths joining the same pair of vertices h...
Abstract. We introduce a new class of countably infinite random geometric graphs, whose vertices V a...
AbstractA graph G is traceable if there is a path passing through all the vertices of G. It is prove...
International audienceA set S of isometric paths of a graph G is "v-rooted", where v is a vertex of ...
A graph is k-indivisible, where k is a positive integer, if the deletion of any finite set of vertic...
AbstractThe paper is concerned with certain kinds of random processes in infinite graphs. A finite t...
summary:Let $G$ be a (finite undirected) connected graph (with no loop or multiple edge). The set $\...
In recent years, considerable advances have been made in the study of properties of metric spaces in...
For an undirected graph G¿=¿(V,E), we say that for l,u,v¿¿¿V, l separates u from v if the distance b...
A class of countable infinite graphs with unbounded vertex degree is con-sidered. In these graphs, t...
Given an input undirected graph G=(V,E), we say that a vertex l separates u from v (where u,v ¿ V) i...