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Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments

Hortensia Galeana-Sanchez, Rocío Rojas-Monroy (2008)

Discussiones Mathematicae Graph Theory

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u,v ∈ N there is no monochromatic...

Monomial ideals with tiny squares and Freiman ideals

Ibrahim Al-Ayyoub, Mehrdad Nasernejad (2021)

Czechoslovak Mathematical Journal

We provide a construction of monomial ideals in R = K [ x , y ] such that μ ( I 2 ) < μ ( I ) , where μ denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in the ring R , we generalize the definition of a Freiman ideal which was introduced in J. Herzog, G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case of this characterization leads to some further investigations on μ ( I k ) that generalize some results...

Monomial subdigraphs of reachable and controllable positive discrete-time systems

Rafael Bru, Louis Caccetta, Ventsi Rumchev (2005)

International Journal of Applied Mathematics and Computer Science

A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents....

Monomorphisms in spaces with Lindelöf filters

Richard N. Ball, Anthony W. Hager (2007)

Czechoslovak Mathematical Journal

𝐒𝐩𝐅𝐢 is the category of spaces with filters: an object is a pair ( X , ℱ ) , X a compact Hausdorff space and ℱ a filter of dense open subsets of X . A morphism f ( Y , 𝒢 ) → ( X , ℱ ) is a continuous function f Y → X for which f - 1 ( F ) ∈ 𝒢 whenever F ∈ ℱ . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically address only one of these...

Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak (2014)

Annales mathématiques Blaise Pascal

In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of z = 0 . Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.

Monte Carlo simulation and analytic approximation of epidemic processes on large networks

Noémi Nagy, Péter Simon (2013)

Open Mathematics

Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic...

Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix

Hiroshi Kurata, Ravindra B. Bapat (2016)

Special Matrices

By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix B, and vice...

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