104,386 research outputs found
Amid.cero9 on the Representation of Architecture: Efrén G Grinda and Cristina Díaz Moreno in conversation with Anne Elisabeth Toft and Christina Capetillo
No full textAnother step towards proving a conjecture by Plummer and Toft
No full textAbstractA cyclic colouring of a graph G embedded in a surface is a vertex colouring of G in which any two distinct vertices sharing a face receive distinct colours. The cyclic chromatic number χc(G) of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 [M.D. Plummer, B. Toft, Cyclic coloration of 3-polytopes, J. Graph Theory 11 (1987) 507–515] conjectured that χc(G)≤Δ∗+2 for any 3-connected plane graph G with maximum face degree Δ∗. It is known that the conjecture holds true for Δ∗≤4 and Δ∗≥24. The validity of the conjecture is proved in the paper for Δ∗≥18
Exhibition of oil paintings and water-colour drawings of Newfoundland, and some English pictures
No full textThis is a catalogue from an exhibition of pieces by artist Alfonso Toft, held at Walker's Galleries, London, in 1920. Included in the exhibition are English landscapes and works created from Toft's expedition to Newfoundland. Toft was the guest of Lord Rothmere, who was instrumental in the creation of several paper mills in Newfoundland, and so the dominating subjects of Toft's Newfoundland pieces are the paper mills and surrounding landscapes
Unsolved graph colouring problems
No full textOur book Graph Coloring Problems [85] appeared in 1995. It contains descriptions of unsolved problems, organized into sixteen chapters. A large number of publications on graph colouring have appeared since then, and in particular around thirty of the 211 problems in that book have been solved. In this chapter we review some of our favourite problems that remain unsolved. Introduction A main reason for the continued interest in the area of graph colouring is its wealth of interesting unsolved problems. Many of these are easy to state, but seemingly difficult to solve. However they are not impossible, as the literature in the field will testify. The seven most striking results of the past twenty years are: • the 5-list-colourability of planar graphs (dating back to V. G. Vizing in 1975 and to P. Erdős, A. L. Rubin and H. Taylor in 1979) by Thomassen [159] • the confirmation by Robertson, Sanders, Seymour and Thomas [137] of the truth of the four-colour theorem (F. Guthrie and A. De Morgan (1852)) • the asymptotic solution by Reed [134] of the problem as to whether for k ≥ 9 there are k-chromatic graphs without complete k-graphs and of maximum degree k (V. G. Vizing (1968) and O. V. Borodin and A. V. Kostochka (1977)) • the proof by Chudnovsky, Robertson, Seymour and Thomas [39] of the strong perfect graph conjecture of C. Berge around 1960 • the proof by Thomassen [161] of the weak 3-flow conjecture of W. T. Tutte (1954) and F. Jaeger (1988) • the solution by Kostochka and Yancey [111] to the problem of critical graphs with few edges (due to T. Gallai (1963) and O. Ore (1967)) • the description found by Borodin, Dvořák, Kostochka, Lidický and Yancey [24] of all 4-critical planar graphs with exactly four triangles (B. Grünbaum (1963), V. A. Aksenov (1974) and P. Erdős (1990)). In addition to these major achievements there are many other important results – in fact, thirty-one of the original 211 problems from the lists in Jensen and Toft [85] were solved by 2013.</p
Even cycles in graphs
No full textLet G be a 3-connected simple graph of minimum degree 4 on at least six vertices. The author proves the existence of an even cycle C in G such that G-V ( C ) is connected and G-E ( C ) is 2-connected. The result is related to previous results of Jackson, and Thomassen and Toft. Thomassen and Toft proved that G contains an induced cycle C such that both G-V ( C ) and G-E ( C ) is 2-connected. G does not in general contain an even cycle such that G-V ( C ) is 2-connected. © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 163–223, 2004Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34893/1/10156_ftp.pd
Non-separating induced cycles in graphs
No full textIn this paper we consider non-separating induced cycles in graphs. A basic result is that any 2-connected graph with at least six vertices and without such a cycle has at least four vertices of degree 2, and this is best possible. For any 3-connected graph G we prove that there exists a non-separating induced cycle C, such that all cycles in G-V(C) are contained in the same block of G-V(C). We apply our results in various directions. In particular, we obtain an extension of a conjecture of Hobbs (first proved by Jackson), and a new proof of Tutte's theorem on 3-connected graphs. Moreover, we show that any graph with minimum degree at least 3 contains a subdivision of K4 in which the three edges of a Hamiltonian path of the K4 are left undivided. This is an extension of a conjecture by Toft and implies an extension of a conjecture of Bollobás and Erdös (first proved by Larson) on the existence of an odd cycle with at least one diagonal. Finally, we obtain a result on the existence of a vertex joined by edges to three vertices of a cycle in a graph. This implies an extremal result conjectured by Bollobás and Erdös (first proved by Thomassen), as well as the conjecture of Toft that every 4-chromatic graph contains such a configuration
Bibliographie Hilarion G. Petzold 1958 – 2009 mit Anhang als Einführung
No full textDieses Archiv enthält die Gesamtbibliographie der Werke des Autors nebst einiger Texte „Über H. G. Petzold“ im Schlussteil der Bibliographie sowie einen Anhang mit einer Einführung in die Architektur des Werkes in seinem wissenslogischen Aufbau als Ausarbeitung seines „Tree of Science Modells“ (2007).This archive contains the complete bibliography of the author and some texts about H. G. Petzold, moreover an epilogue with an introduction to the architecture of the works in its epistemological structure and composition and as an elaborations of Petzold’s „Tree of Science Modell (2007).https://www.fpi-publikation.de/polyloge/01-2009-petzold-h-g-gesamtbibliographie-h-g-petzold-1958-2009-updating-november2009/peerReviewedpublishedVersio
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
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3346: Samuel G. Freedman, author, 2013
No full textPhotograph of author Samuel G. Freedman, at NT Daily Slash meeting in the Mayborn School of Journalism at UNT
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