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Acyclic edge colourings of graphs with large girth
(20161103)
Article
Open AccessAn edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every e > 0, there exists a g = g(e) such that if G has maximum degree ¿ and girth at least ... 
Connectivity in bridgeaddable graph classes: the McDiarmidStegerWelsh conjecture
(20180917)
Article
Restricted access  publisher's policyA class of graphs is bridgeaddable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, ... 
Perturbed marked reduced forms of invariant subspaces
(Elsevier, 20181215)
Article
Restricted access  publisher's policyThe classification of invariant subspaces is an open problem related to other important ones like the Carlson problem. Here we obtain a reduced form of these invariant subspaces as a new tool to tackle these problems. In ... 
Structural stability of pairs of matrices under contragredient equivalence
(2019)
Article
Restricted access  publisher's policyA complex matrix pencil A¿B is called structurally stable if there exists its neighborhood in which all pencils are strictly equivalent to this pencil. We describe all complex matrix pencils that are structurally stable. ... 
Asymptotic density of collision orbits in the restricted circular planar 3 body problem
(20190312)
Article
Restricted access  publisher's policyFor the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(µ120) dense as µ¿0 . 
Fast recoloring of sparse graphs
(20150907)
Article
Open AccessIn this paper, we show that for every graph of maximum average degree bounded away from d and any two (d + 1)colorings of it, one can transform one coloring into the other one within a polynomial number of vertex recolorings ... 
Large subgraphs without short cycles
(20150106)
Article
Open AccessWe study two extremal problems about subgraphs excluding a family F of graphs. i) Among all graphs with m edges, what is the smallest size f(m, F) of a largest F–free subgraph? ii) Among all graphs with minimum degree d ... 
Decomposition of bounded degree graphs into C4free subgraphs
(20141015)
Article
Open AccessWe prove that every graph with maximum degree ∆ admits a partition of its edges into O(√∆) parts (as ∆→∞) none of which contains C4 as a subgraph. This bound is sharp up to a constantfactor. Our proof uses an iterated ... 
A gradient estimate for nonlocal minimal graphs
(20190401)
Article
Restricted access  publisher's policyWe consider the class of measurable functions defined in all of Rn that give rise to a nonlocal minimal graph over a ball of Rn. We establish that the gradient of any such function is bounded in the interior of the ball ... 
Fault detection based on Lyapunov exponents estimation for stabilized mechanicaln systems
(201904)
Article
Open AccessWe study a stabilizable mechanical system in the vicinity of an equilibrium position. This position, as a rule, is unstable, and the system is underactuated. It is assumed that faults affect the technical process and its ... 
Impulsive control realization applied to nondissipative first order plants: an academic electronic implementation
(WSEAS Press, 20190402)
Article
Open AccessImpulsive control design is a control strategy mainly based on the impulsive differential model of the plant to be stabilized. Hence, this system should have at least one state variable able to be driven by impulsive ... 
Robust sliding mode control of a DC/DC Boost converter with switching frequency regulation
(20180101)
Article
Restricted access  publisher's policyThis paper presents the design of a hysteresis band controller to regulate the switching frequency in a sliding mode controlled nonlinear Boost power converter. The proposed architecture relies on a piecewise linear modeling ...