Let (G,C) be an edge-colored bipartite graph with bipartition (X,Y ). A heterochromatic matching of G is such a matching in which no two edges have the same color. Let N c(S) denote a maximum color neighborhood of S ⊆ V (G). We show that if |N c(S)| ≥ |S| for all S ⊆ X, then G has a heterochromatic matching with cardinality at least d |X| 3 e. We also obtain that if |X| = |Y | = n and |N c(S)| ...

Expanders are classes of highly connected graphs that are of fundamental importance in graph theory, with numerous applications, especially in theoretical computer science [29]. While the literature contains various definitions of expanders, this paper focuses on bipartite expanders. For ∈ (0, 1], a bipartite graph G with bipartition V (G) = A ∪ B is a bipartite -expander if |A| = |B| and |N(S)...

Let (G,C) be an (edge-)colored bipartite graph with bipartition (X, Y ) and |X| = |Y | = n. A heterochromatic matching of G is such a matching in which no two edges have the same color. Let N c(S) denote a maximum color neighborhood of S ⊆ V (G). In a previous paper, we showed that if N c(S) ≥ |S| for all S ⊆ X or S ⊆ Y , then G has a heterochromatic matching with cardinality at least d3n−1 8 e...

is paper presents results of a control annotation of the Topic-Focus Articulation of Czech sentences based on the notion of “aboutness”. is is one of the steps testing the hypothesis about the relation between contextual boundness and “aboutness”. We suppose that the bipartition of the sentence into its Topic and Focus (“aboutness”) can be automatically derived from the values of contextual b...

Abstract: Let G = (VG, EG) be a simple connected graph. The eccentric distance sum of G is defined as ξ(G) = ∑ v∈VG εG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v) = ∑ u∈VG dG(u, v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number γ having the minimal eccentric distance sum is determined and the tree among n-...

Non-impeding noisy-And Trees (NATs) provide a general, expressive, and efficient causal model for conditional probability tables (CPTs) in discrete Bayesian networks (BNs). A BN CPT may either be directly expressed as a NAT model or be compressed into one. Once CPTs in BNs are so expressed or compressed, complexity of inference (both space and time) can be significantly reduced. The most import...

We extend the work of Letchford [Letchford, A. N. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25 443–454] by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the m...

‎a total dominating set of a graph $g$ is a set $d$ of vertices of $g$ such that every vertex of $g$ has a neighbor in $d$‎. ‎the total domination number of a graph $g$‎, ‎denoted by $gamma_t(g)$‎, ‎is~the minimum cardinality of a total dominating set of $g$‎. ‎chellali and haynes [total and paired-domination numbers of a tree, akce international ournal of graphs and combinatorics 1 (2004)‎, ‎6...

Let (B,C) be an (edge-)colored bipartite graph with bipartition (X,Y ), i.e., B is assigned a mapping C : E(B) → {1, 2, · · · , r}, the set of colors. A matching of B is called heterochromatic if its any two edges have different colors. Let N (S) denote a maximum color neighborhood of S ⊆ V (B). We show that if |N (S)| ≥ |S| for all S ⊆ X, then B contains a heterochromatic matching with cardina...

1 The First Counterexample Let ρ be a quantum state on the space (C) of n qudits (d-dimensional quantum systems). Denote by ρS the reduced state of ρ onto some subset S of the qudits. We partition S further into two nonempty subsets of qudits A and A := S\A (thus S must contain at least two qudits). Denote by Sep(A) the convex set of quantum states which are bipartite separable on S across the ...