It is well known that a graph is bipartite if and only if the spectrum of its adjacency matrix is symmetric. In the present paper, this assertion is dissected into three separate matrix results of wider scope, which are extended also to hypermatrices. To this end the concept of bipartiteness is generalized by a new monotone property of cubical hypermatrices, called odd-colorable matrices. It is...

This paper surveys some recent results on the generation of implicitly given hypergraphs and their applications in Boolean and integer programming, data mining, reliability theory, and combinatorics. Given a monotone property π over the subsets of a finite set V , we consider the problem of incrementally generating the family Fπ of all minimal subsets satisfying property π, when π is given by a...

It is shown that the inverse limit of an inverse system of smooth continua is a smooth continuum provided that there exists a thread composed of initial points and that the bonding mappings are monotone relative to these points. It also is proved that the property of being an arboroid, a dendroid, a generalized tree, a fan or a smooth fan is an invariant under the inverse limit operation if the...

We prove some new results about the existence of solutions of variational inequalities with quasilinear operators having the generalized pseudo-monotone property. We also consider the case where data are Radon measures or L 1 elements.

We consider the question of how well a given distribution can be approximated with probabilistic graphical models. We introduce a new parameter, effective treewidth, that captures the degree of approximability as a tradeoff between the accuracy and the complexity of approximation. We present a simple approach to analyzing achievable tradeoffs that exploits the threshold behavior of monotone gra...

Coalgebras provide a uniform framework for the semantics of a large class of (mostly non-normal) modal logics, including e.g. monotone modal logic, probabilistic and graded modal logic, and coalition logic, as well as the usual Kripke semantics of modal logic. In earlier work, the finite model property for coalgebraic logics has been established w.r.t. the class of all structures appropriate fo...

In this paper we define, for a graph invariant ψ, the deck ratio of ψ by Dψ(G) = ψ(G) P v∈V (G) ψ(G−v) . We give generic upper and lower bounds on Dψ for monotone increasing and monotone decreasing invariants ψ, respectively. Then we proceed to consider the Wiener index W (G), showing that DW (G) ≤ 1 |V (G)|−2 . We show that equality is attained for a graph G if and only if every induced P3 sub...

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P (x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P (x+ 1), which leads to the log-concavity of P (x+ c) for any c ≥ 1 due to Llamas and Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...

March-April RANDOM COINCIDENCE POINTS FOR MULTI-VALUED NON-LINEAR CONTRACTIONS IN PARTIALLY ORDERED METRIC SPACES N. Shafqat , N. Yasmin , Z. Akhter c a,b Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800,Pakistan. c Department of Mathematics, The Islamia University Bhawalpur [email protected], [email protected], [email protected] A...

A graph G = (V,E) is said to be saturated with respect to a monotone increasing graph property P, if G / ∈ P but G ∪ {e} ∈ P for every e ∈ ( V 2 ) \ E. The saturation game (n,P) is played as follows. Two players, called Mini and Max, progressively build a graph G ⊆ Kn, which does not satisfy P. Starting with the empty graph on n vertices, the two players take turns adding edges e ∈ ( V (Kn) 2 )...