Complexity of colouring problems restricted to unichord-free and \{square,unichord\}-free graphs

A \emph{unichord} in a graph is an edge that is the unique chord of a cycle. A \emph{square} is an induced cycle on four vertices. A graph is \emph{unichord-free} if none of its edges is a unichord. We give a slight restatement of a known structure theorem for unichord-free graphs and use it to show that, with the only exception of the complete graph $K_4$, every square-free, unichord-free graph of maximum degree~3 can be total-coloured with four colours. Our proof can be turned into a polynomial time algorithm that actually outputs the colouring. This settles the class of square-free, unichord-free graphs as a class for which edge-colouring is NP-complete but total-colouring is polynomial

Lake Area Variability Across a Climatic and Vegetational Transect in Southeastern Alberta

Areas of 34 small lakes forming a transect across the southern margin of the Boreal Forest into the Grassland in southern Alberta were obtained from 326 aerial photographs, with at least six photographs for each lake in different months and different years from 1949 to 1992. Standard deviations of standardised lake areas (used as an index of lake area sensitivity to short term climate fluctuations) were plotted against a climatic moisture index; the resulting scatter of points is constrained by a function relating lake sensitivity to long-term regional climatic moisture. The lakes show high sensitivity in the Grassland where potential évapotranspiration exceeds precipitation, a steep drop in sensitivity over a small range of climatic moisture values in the Aspen Parkland, and very low sensitivity in the Boreal Forest where precipitation exceeds potential évapotranspiration.Les superficies de 34 petits lacs constituant un transect à partir de la limite méridionale de la forêt boréale jusqu'à la prairie, dans le sud de l'Alberta. ont été calculées grâce à l'étude de 326 photographies aériennes. Chacun des lacs comptaient au moins six photographies prises à différents mois et échelonnées de 1949 à 1992. Les écarts types de la superficie standardisée des lacs (employés comme indice de la sensibilité de la superficie des lacs aux fluctuations climatiques à court terme) ont été reportés par rapport à l'indice d'humidité. Le nuage de points qui en résulte est commandé par la fonction reliant la sensibilité des lacs à l'humidité du climat régional. Les lacs démontrent une grande sensibilité en prairie où l'évapotranspiration potentielle excède les précipitations, une très forte baisse de sensibilité dans la tremblaie-parc et une très faible sensibilité dans la forêt boréale où les précipitations excèdent l'évapotranspiration potentielle.Die Ausdehnungen von 34 kleinen Seen, welche ein Transect von der sùdlichen Grenze des nôrdlichen Waldgùrtels bis zur Prârie bilden, wurden mittels 326 Luftaufnahmen berechnet; dabei hat man mindestens sechs Aufnahmen fur jeden See gemacht, in verschiedenen Monaten und verschiedenen Jahren von 1949 bis 1992. Die Standardabweichungen von den standardisierten Seen-Oberflàchen (welche als Gradmesser fur die Sensibilitàt der Seen-Oberflâchen auf kurzfristige klimatische Schwankungen benutzt wurden) hat man in Bezug auf den klimatischen Feuchtigkeitsindex ubertragen: die hierdurch erzielte Streuung von Punkten ist durch die Funktion bestimmt, welche die Seen-Sensibilitât mit langzeitiger regionaler klimatischer Feuchtigkeit verbindet. Die Seen weisen eine hohe Sensibilitàt in der Prârie auf, wo die potentielle Evapotranspiration die Niederschlàge ùbertrifft, eine jâhe Abnahme der Sensibilitàt ùber einer kleinen Reihe von klimatischen Feuchtig-keitswerten im Aspen Parkland, und sehr niedrige Sensibilitàt im nôrdlichen WaIdgùrtel, wo die Niederschlàge hoher als die potentielle Evapotranspiration sind

The complexity of clique graph recognition

A complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote by C (G) the clique family of G. The clique graph of G, denoted by K (G), is the intersection graph of C (G). Say that G is a clique graph if there exists a graph H such that G = K (H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete.Facultad de Ciencias Exacta

The complexity of clique graph recognition

A complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote by C (G) the clique family of G. The clique graph of G, denoted by K (G), is the intersection graph of C (G). Say that G is a clique graph if there exists a graph H such that G = K (H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete.Facultad de Ciencias Exacta

Maximum Cut on Interval Graphs of Interval Count Four Is NP-Complete

The computational complexity of the MaxCut problem restricted to interval graphs has been open since the 80's, being one of the problems proposed by Johnson on his Ongoing Guide to NP-completeness, and has been settled as NP-complete only recently by Adhikary, Bose, Mukherjee and Roy. On the other hand, many flawed proofs of polynomiality for MaxCut on the more restrictive class of unit/proper interval graphs (or graphs with interval count 1) have been presented along the years, and the classification of the problem is still unknown. In this paper, we present the first NP-completeness proof for MaxCut when restricted to interval graphs with bounded interval count, namely graphs with interval count 4

Endemic pemphigus foliaceus (fogo selvagem) and pemphigus vulgaris: immunoglobulin G heterogeneity detected by indirect immunofluorescence

Pemphigus are autoimmune intraepidermal blistering diseases in which immunoglobulin G (IgG) autoantibodies are directed against desmosomal glycoproteins. The aim of this study was to determine the IgG subclass profile of endemic pemphigus foliaceus (fogo selvagem) and pemphigus vulgaris utilizing indirect immunofluorescence. PATIENTS AND METHODS: Twenty-five patients with pemphigus vulgaris, 25 with endemic pemphigus foliaceus (fogo selvagem), and 25 healthy controls were analyzed by indirect immunofluorescence for circulating autoantibodies (total IgG and its subclasses). RESULTS: Our data revealed a significant correlation (PPênfigos são enfermidades auto-imunes bolhosas intraepidérmicas, onde auto-anticorpos IgG se dirigem contra glicoproteínas desmossomais. O objetivo deste estudo foi determinar o perfil de subclasses de imunoglubulina G no pênfigo foliáceo endêmico (fogo selvagem) e no pênfigo vulgar através da imunofluorescência indireta. MÉTODOS: Vinte e cinco doentes de pênfigo foliáceo endêmico (fogo selvagem), 25 de pênfigo vulgar e 25 controles sadios foram analisados através da imunofluorescência indireta, com respeito aos auto-anticorpos circulantes (imunoglobulina G total e subclasses). RESULTADOS: Nossos dados mostram uma correlação estatisticamente significativa (

Comparing Diagnostic Performance of Short and Long [18F]FDG-PET Acquisition Times in Giant Cell Arteritis

(1) Background: In giant cell arteritis (GCA), the assessment of cranial arteries using [ 18F]fluorodeoxyglucose ([ 18F]FDG) positron emission tomography (PET) combined with low-dose computed tomography (CT) may be challenging due to low image quality. This study aimed to investigate the effect of prolonged acquisition time on the diagnostic performance of [ 18F]FDG PET/CT in GCA. (2) Methods: Patients with suspected GCA underwent [ 18F]FDG-PET imaging with a short acquisition time (SAT) and long acquisition time (LAT). Two nuclear medicine physicians (NMPs) reported the presence or absence of GCA according to the overall image impression (gestalt) and total vascular score (TVS) of the cranial arteries. Inter-observer agreement and intra-observer agreement were assessed. (3) Results: In total, 38 patients were included, of whom 20 were diagnosed with GCA and 18 were without it. Sensitivity and specificity for GCA on SAT scans were 80% and 72%, respectively, for the first NMP, and 55% and 89% for the second NMP. On the LAT scans, these values were 65% and 83%, and 75% and 83%, respectively. When using the TVS, LAT scans showed especially increased specificity (94% for both NMPs). Observer agreement was higher on the LAT scans compared with that on the SAT scan. (4) Conclusions: LAT combined with the use of the TVS may decrease the number of false-positive assessments of [ 18F]FDG PET/CT. Additionally, LAT and TVS may increase both inter and intra-observer agreement. </p