Given a monomial m in polynomial ring and subset L of the variables ring, principal -Borel ideal generated by is all monomials which can be obtained from successively replacing those are have smaller index. collection I = { 1 , … r } where i for (where subsets may different each ideal), we prove essence that if bipartite incidence graph among chordal bipartite, then defining equations multi-Ree...

In this paper, we give a fast algorithm for constructing a Galois lattice of a binary relation. When the binary relation is represented as a bipartite graph, each vertex of the lattice (called a concept) corresponds to a maximal bipartite clique of the bipartite graph. Thus, our algorithm also enumerates all maximal bipartite cliques. Further, our algorithm can be naturally modified to compute ...

These problems are inspired by a careful study of the papers of concerning bipartite distance-regular graphs. Throughout these notes we let Γ = (X, R) denote a bipartite distance-regular graph with diameter D ≥ 3 and standard module V = C X. We fix a vertex x ∈ X and let E denote the corresponding dual primitive idempotents. We define the matrices R = D i=0 E * i+1 AE * i , L= D i=0 E * i−1 AE ...

Let (P ,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = ⋃ x∈X{y : yIx} and by [X ] = (X)I ∪ X . With this terminology a partial linear space (P ,L, I) is said to admit a (1,≤ k)-identifying code if and only if the sets [X ] are mutually different for all X ⊆ P ∪L with |X | ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)...

Given a distribution G over labeled bipartite (multi) graphs, G = (W; M; E) where jWj = jMj = n, let L(n) denote the size of the largest planar matching of G (here W and M are posets drawn on the plane as two ordered rows of nodes, an upper and a lower one, and a (w; m) edge is drawn as a straight line between w and m). The main focus of this work is to understand the asymptotic (in n) behavior...

Let G be a bipartite graph with vertex parts of orders N and M , and X edges. I prove that if G has no cycles of length 2l, for all l ∈ [2, 2k], and N ≥ M , then X < M 1 2 N k+1 2k + O(N).

The Moore bipartite bound represents an upper bound on the order of a bipartite graph of maximum degree ∆ and diameterD. Bipartite graphs of maximum degree ∆, diameterD and order equal to the Moore bipartite bound are called Moore bipartite graphs. Such bipartite graphs exist only if D = 2, 3, 4 and 6, and for D = 3, 4, 6, they have been constructed only for those values of ∆ such that ∆− 1 is ...

The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...

We shall prove that if L is a 3-chromatic (so called "forbidden") graph, and -R" is a random graph on n vertices, whose edges are chosen indepen-6" is a bipartite subgraph of R" of maximum size, -F" is an L-free subgraph of R" of maximum size, dently, with probability p, and then (in some sense) F" and 6" are very near to each other: almost surely they have almost the same number of edges, and ...

In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V, E) with n vertices with a color (or label) function L : E → {c1, . . . , cq}, the labeled maximum matching problem consists in finding a maximum matching on G that uses a minimum or a maximum number of colors.