A graph with signed edges is orientation embedded in a surface when it is topologically embedded so that one trip around a closed path preserves or reverses orientation according as the path's sign product is positive or negative. We nd the smallest surface within which it is possible to orientation-embed the complete bipartite signed graph K r;s , which is obtained from the complete bipartite ...

‎in this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of villarreal on bipartite graphs‎. ‎for bipartite graphs two‎ ‎different characterizations were given by ravindra and villarreal‎. ‎we show that these two characterizations imply each other‎.

We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We find that the response is double-peaked, independantly of the details of boundary conditions. The two peaks lie precise...

Let Γ denote the spaces of all double entire sequences. Let Λ denote the spaces of all double analytic sequences. This paper is devoted to a study of the general properties of Nörlund double entire sequence space η ( Γ ) , Γ and also study some of the properties of η ( Γ ) and η ( Λ ) .

We show that any graph that contains k edge-disjoint double rays for any k ∈ N contains also infinitely many edge-disjoint double rays. This was conjectured by Andreae in 1981.

A (p, 1)-total labelling of a graph G = (V,E) is a total coloring L from V ∪ E into {0, . . . , l} such that |L(v) − L(e)| ≥ p whenever an edge e is incident to a vertex v. The minimum l for which G admits a (p, 1)-total labelling is denoted by λp(G). The case p = 1 corresponds to the usual notion of total colouring, which is NP-hard to compute even for cubic bipartite graphs [6]. In this paper...

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l1 or l∞ norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l1 and l∞ norms. It has been proved that the inverse maximum-we...

A theorem of A. Schrijver asserts that a d–regular bipartite graph on 2n vertices has at least ( (d− 1)d−1 dd−2 )n perfect matchings. L. Gurvits gave an extension of Schrijver’s theorem for matchings of density p. In this paper we give a stronger version of Gurvits’s theorem in the case of vertex-transitive bipartite graphs. This stronger version in particular implies that for every positive in...

K e y w o r d s P l a n e graph, Outerplane graph, Bipartite graph, Perfect matching, Z-transformation graph. 1. I N T R O D U C T I O N A graph G is a planar graph if it can be embedded in plane such that edges only intersect at their end vertices. A plane graph is such an embedding. A plane graph is called an outerplane graph if all vertices are lie on the boundary of the exterior face. A gra...

A bipartite graph G = (L,R;E) with at least one edge is said to be identifiable if for every vertex v ∈ L, the subgraph induced by its non-neighbors has a matching of cardinality |L|− 1. This definition arises in the context of low-rank matrix factorization and is motivated by signal processing applications. In this paper, we study the resilience of identifiability with respect to edge addition...