A bipartite graph G = (L,R;E) 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. Motivated by signal processing applications, in this paper we (i) propose the robustness of identifiability with respect to edge modifications as a polynomially...

Based on an acyclic orientation of the Z-transformation graph, a finite distributive lattice (FDL for short)M(G) is established on the set of all 1-factors of a plane (weakly) elementary bipartite graph G. For an FDL L, if there exists a plane bipartite graph G such that L is isomorphic to M(G), then L is called a matchable FDL. A natural question arises: Is every FDL a matchable FDL? In this p...

In a symmetric independent private values setting a sealed-bid double auction dissolves a partnership e¢ciently. This well known result remains valid in a model with interdependent valuations. However, if the interdependent components of valuations are large agents might prefer not to participate in a double auction. Therefore a simple extention of the rules of double-auctions is suggested that...

We modify W. Vickrey's (1961, J. Finance 16, 8 37) mechanism for call markets by introducing the participation stage and study the efficiency properties of the modified mechanism. We provide sufficient conditions under which the modified Vickrey double auction achieves full efficiency. In addition, we prove that the modified Vickrey double auction achieves asymptotic efficiency even when full e...

Let G = (L,R; E) be a bipartite graph such that V (G) = L ∪ R, |L| = p and |R| = q. G is called (p, q)-tree if G is connected and |E(G)| = p + q − 1. Let G = (L, R;E) and H = (L′, R′;E′) be two (p, q)-tree. A bijection f : L ∪ R → L′ ∪ R′ is said to be a biplacement of G and H if f(L) = L′ and f(x)f(y) / ∈ E′ for every edge xy of G. A biplacement of G and its copy is called 2-placement of G. A ...

We prove a new sufficient conditi()n on degrees for a bipartite tournament to be Hamiltonian, that is, if an n x n bipartite tournament T satisfies the condition dT(u) + dj;(v) ~ n 1 whenever uv is an arc of T, then T is Hamiltonian, except for two exceptional graphs. This result is shown to be best possible in a sense. T(X, Y, E) denotes a bipartite tournament with bipartition (X, Y) and verte...

the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 26 (2010) 95--105‎.]. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...

For a set of non-negative integers L, the L-intersection number of a graph is the smallest number l for which there is an assignment of subsets Av ⊆ {1, . . . , l} to vertices v, such that every two vertices u, v are adjacent if and only if |Au ∩ Av| ∈ L. The bipartite L-intersection number is defined similarly when the conditions are considered only for the vertices in different parts. In this...

Let G = (V ,E) be a simple connected graph and λ1(G) be the largest Laplacian eigenvalue of G. In this paper, we prove that: 1. λ1(G) = max{du +mu : u ∈ V } if and only if G is a regular bipartite or a semiregular bipartite graph, where du and mu denote the degree of u and the average of the degrees of the vertices adjacent to u, respectively. 2. λ1(G) = 2 + √ (r − 2)(s − 2) if and only if G is...