The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or, more generally, the complete k-partite graph. Lifting is a central tool to ...

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this ...

Given a graph G = (V,E), an L(δ1, δ2, δ3)-labeling is a function f assigning to nodes of V colors from a set {0, 1, . . . , kf} such that |f(u) − f(v)| ≥ δi if u and v are at distance i in G. The aim of the L(δ1, δ2, δ3)-labeling problem consists of finding a coloring function f such that the value of kf is minimum. This minimum value is called λδ1,δ2,δ3(G). In this paper we study this problem ...

Abstract: A graph G with p vertices is said to be strongly multiplicative if the vertices of G can be labeled with p consecutive positive integers 1, 2, ..., p such that label induced on the edges by the product of labels of end vertices are all distinct. In this paper we investigate strongly multiplicative labeling of some snake related graphs. We prove that alternate triangular snake and alte...

A circular-arc graph G is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model ...

Using graph theoretic techniques, it is shown that the height characteristic of a triangular matrix A majorizes the dual sequence of the sequence of differences of maximal cardinalities of singular k-paths in the graph G(A) of A and that in the generic case the height characteristic is equal to that dual sequence. The results on matrices are also used to prove a graph theoretic result on the du...