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Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f (k) vertices whenever k ≤ (n − f (k))/2. This is a common generalization of vertex connectivity (when f is constant) and expansion (when f is linear). We show that an f-connected graph contains a cycle of length linear in n if f is(More)
BACKGROUND Transcranial magnetic stimulation (TMS) is the only noninvasive method for presurgical stimulation mapping of cortical function. Recent technical advancements have significantly increased the focality and usability of the method. OBJECTIVE To compare the accuracy of a 3-dimensional magnetic resonance imaging-navigated TMS system (nTMS) with the(More)
In the class of k-connected claw-free graphs, we study the stability of some hamilto-nian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these properties there is an innnite family of graphs G k of(More)
In the present study repetitive transcranial magnetic stimulation (rTMS) was utilised to interrupt neural activity in selected cortical areas at several different time periods while participants performed a stimulus-response correspondence (SRC) task. Responses are usually faster and less error-prone when stimulus (S) and response (R) features correspond(More)
With the present study we investigated cue-induced preparation in a Simon task and measured electroencephalogram and functional magnetic resonance imaging (fMRI) data in two within-subjects sessions. Cues informed either about the upcoming (1) spatial stimulus-response compatibility (rule cues), or (2) the stimulus location (position cues), or (3) were(More)
We introduce the concept of an edge-colouring total k-labelling. This is a labelling of the vertices and the edges of a graph G with labels 1, 2,. .. , k such that the weights of the edges define a proper edge colouring of G. Here the weight of an edge is the sum of its label and the labels of its two endvertices. We define χ ′ t (G) to be the smallest(More)