124,827 research outputs found
Gallai and anti-Gallai graphs of a graph
No full textsummary:The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be -free for any finite graph . The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained
GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH
No full textAbstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai
graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs
and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement
reducible graphs-cographs is discussed in detail. Some relations between the chromatic
number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are
also obtained
Acupressure therapy for insomnia in adolescents: a polysomnographic study
No full textMarco Carotenuto,1 Beatrice Gallai,2 Lucia Parisi,3 Michele Roccella,3 Maria Esposito11Sleep Clinic for Developmental Age, Clinic of Child and Adolescent Neuropsychiatry, Second University of Naples, Naples, 2Unit of Child and Adolescent Neuropsychiatry, University of Perugia, Perugia, 3Child Neuropsychiatry, Department of Psychology, University of Palermo, Palermo, ItalyBackground: The purpose of this study was to assess the efficacy of acupressure therapy in a sample of adolescents with insomnia using a standard polysomnographic evaluation.Methods: For this study, 25 adolescents affected by psychophysiological insomnia (mean age 15.04 ± 1.18 years, 12 boys) were enrolled. A device known as the Sea-Band® was used by the patients in order to improve their symptoms related to difficulty in falling asleep. All subjects enrolled underwent two sets of consecutive overnight polysomnographic studies in the Sleep Laboratory of the Clinic of Child and Adolescent Neuropsychiatry, comprising two studies at baseline (before treatment) and another two studies at the end of 6 months of treatment.Results: At the end of 6 months of treatment, there was a significant increase in all macrostructural parameters of sleep duration, and a reduction in sleep onset latency, wake after sleep onset, and stage 2 sleep. Moreover, the study group showed a significant increase in percent sleep efficiency (P < 0.001) and in slow wave sleep representation.Conclusion: Acupressure is a noninvasive, safe, and effective method for the management of insomnia in adolescents, with good compliance and no adverse effects.Keywords: insomnia, adolescence, acupressure, polysomnograph
Extended Gallai\u27s Theorem
No full textLet G and H be graphs. We say G is H-critical, if every proper subgraph of G except G itself is homomorphic to H. This generalizes the widely known concept of k-color-critical graphs, as they are the case H = Kk - 1. In 1963 [T. Gallai, Kritiche Graphen, I., Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963), 373-395], Gallai proved that the vertices of degree k in a Kk-critical graph induce a subgraph whose blocks are either odd cycles or complete graphs. We generalize Gallai\u27s Theorem for every H-critical graph, where H = Kk - 2 + H′, (the join of a complete graph Kk - 2 with any graph H′). This answers one of the two unknown cases of a problem given in [J. Nešetřil, Y. Nigussie, Finite dualities and map-critical graphs on a fixed surface. (Submitted to Journal of Combin. Theory, Series B)]. We also propose an open question, which may be a characterization of all graphs for which Gallai\u27s Theorem holds
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Veralgemeende Sylvester-Gallai Stelling
No full textOns gee 'n algoritmiese bewys vir die kontrapositief van die volgende stelling wat onlangs deur die outeurs bewys is:
Laat S 'n eindige versameling van punte in die vlak wees, met elke punt rooi, blou of met beide kleure gekleur. Veronderstel dat daar vir enige twee verskillende punte A en B in S wat 'n kleur k deel, 'n derde punt in S is wat (o.a.) die kleur anders as k het en wat saamlynig met A en B is. Dan is al die punte in S saamlynig. Hierdie stelling is 'n gemeenskaplike veralgemening van die Sylvester-Gallai Stelling en die Motzkin-Rabin Stelling. ENGLISH: We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors: Let S be a finite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia) the colour different from k and is collinear with A and B. Then all the points in S are collinear. This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem
Hypersomnia in children affected by migraine without aura: a questionnaire-based case-control study
No full textMaria Esposito,1 Michele Roccella,2 Lucia Parisi,2 Beatrice Gallai,3 Marco Carotenuto11Center for Childhood Headache, Unit of Child and Adolescent Neuropsychiatry, Department of Mental Health, Physical, and Preventive Medicine, Second University of Naples, Naples, Italy; 2Child Neuropsychiatry, Department of Psychology, University of Palermo, Palermo, Italy; 3Unit of Child and Adolescent Neuropsychiatry, University of Perugia, Perugia, ItalyBackground: The relationship between sleep and headache is meaningful and complex. Children affected by migraines tend to show many sleep disorders, such as insufficient sleep duration and excessive daytime somnolence. Therefore, the aim of this study is to assess the rate of reported sleep habits and self-reported sleepiness in a large pediatric sample of individuals affected by migraine without aura (MoA).Methods: The study population consisted of 271 children aged between 6 and 13 years affected by MoA. The control group was composed of 305 typically developing children. To assess the sleep habits of all individuals (MoA and control), parents filled out the Sleep Disturbance Scale for Children, and to check the degree of subjective perceived daytime sleepiness, all subjects were administered the Pediatric Daytime Sleepiness Scale.Results: The two study groups were matched for age (P = 0.124), sex distribution (P = 0.775), and body mass index z-score (P = 0.107). Parents of children affected by MoA reported a higher total score of sleep disorder symptoms (P < 0.001), disorders of initiating and maintaining (P < 0.001), and disorders of arousal (P < 0.001) than did parents of controls. No significant differences were found in disorders of excessive somnolence. Conversely, in the Pediatric Daytime Sleepiness Scale, migraine children had higher scores (24.67 ± 3.19 vs 11.94 ± 4.81; P < 0.001) and a reduction in referred total sleep time mean duration (469.83 ± 98.112 vs 527.94 ± 83.02; P < 0.001) than typically developing children.Conclusion: Our study identified differences in sleep habits and found a high prevalence of daytime somnolence in children affected by MoA, suggesting the need for routine sleep screening in the pediatric management of children with migraines.Keywords: excessive daytime sleepiness, drowsiness, sleep disorders, migraine without aura, childre
The Sylvester–Gallai theorem, colourings and algebra
No full textAbstractOur point of departure is the following simple common generalisation of the Sylvester–Gallai theorem and the Motzkin–Rabin theorem: Let S be a finite set of points in the plane, with each point coloured red or blue or with both colours. Suppose that for any two distinct points A,B∈S sharing a colour there is a third point C∈S, of the other colour, collinear with A and B. Then all the points in S are collinear. We define a chromatic geometry to be a simple matroid for which each point is coloured red or blue or with both colours, such that for any two distinct points A,B∈S sharing a colour there is a third point C∈S, of the other colour, collinear with A and B. This is a common generalisation of proper finite linear spaces and properly two-coloured finite linear spaces, with many known properties of both generalising as well. One such property is Kelly’s complex Sylvester–Gallai theorem. We also consider embeddings of chromatic geometries in Desarguesian projective spaces. We prove a lower bound of 51 for the number of points in a three-dimensional chromatic geometry in projective space over the quaternions. Finally, we suggest an elementary approach to the corollary of an inequality of Hirzebruch used by Kelly in his proof of the complex Sylvester–Gallai theorem
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
A short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem
No full textAbstractWe present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem from Hall’s Theorem
- …
