354,146 research outputs found

    Making Kr+1-free graphs r-partite

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    The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1-free graph on n vertices with e(G) > ex(n, Kr+1)– α n2, then one can remove εn2 edges from G to obtain an r-partite graph. Füredi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.This article is published as Balogh J, Clemen FC, Lavrov M, Lidický B, Pfender F. Making Kr+1-free graphs r-partite. Combinatorics, Probability and Computing. 2021;30(4):609-618. doi:10.1017/S0963548320000590

    Making Kr+1-Free Graphs r-partite

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    The Erdos-Simonovits stability theorem states that for all epsilon > 0 there exists alpha > 0 such that if G is a Kr+1-free graph on n vertices with e(G) > ex(n, Kr+1)-alpha n2, then one can remove epsilon n2 edges from G to obtain an r-partite graph. Furedi gave a short proof that one can choose alpha = epsilon. We give a bound for the relationship of alpha and epsilon which is asymptotically sharp as epsilon right arrow 0.This pre-print is made available through arixiv: https://arxiv.org/abs/1910.00028.</p

    Roseland Reads Together, Roseland Free Public Library (Roseland, N.J.), 2002

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    Album chronicling the 30th Anniversary of the Roseland Library's Incorporation. The event was commemorated by a Borough-Wide reading activity. All families were invited to read the same book, "Homer Price" by Robert McCloskey. The festivities on May 11, 2002 at the Library included events from the stories in "Homer Price." A Proclamation from the Mayor regarding this event is issued dated April 23, 2002

    Travel photography

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    ThesisJust as trave llers of past centuries recorded their personal impressions in diaries; the modern day trave ller lIses a camera to record the sight s and events of his Journeys . 2 T ravel photography IS as old as photography itself, with the invention of photography, travellers set out with their primative came ras and started recording the world as neve r be fore . The aim in this dissertatio n is to e xplore the OrIgInS of travel photography; discuss ing some of the pioneers of travel photography . To summa ri ze some of I the categories of travel photography , and the importance of diversity. Many problems were encountered and where possible soluti ons offered. The author will al so discu ss his travels and attempt "to anal yse the images taken during these travels

    Labor Saving Devices, inspired by Homer Price," Display, Roseland Free Public Library (Roseland, N.J.)

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    Album chronicling the 30th Anniversary of the Roseland Library's Incorporation. The event was commemorated by a Borough-Wide reading activity. All families were invited to read the same book, "Homer Price" by Robert McCloskey. The festivities on May 11, 2002 at the Library included events from the stories in "Homer Price." A Proclamation from the Mayor regarding this event is issued dated April 23, 2002

    Roseland Reads Together, Sign, Roseland Free Public Library (Roseland, N.J.), 2002

    No full text
    Album chronicling the 30th Anniversary of the Roseland Library's Incorporation. The event was commemorated by a Borough-Wide reading activity. All families were invited to read the same book, "Homer Price" by Robert McCloskey. The festivities on May 11, 2002 at the Library included events from the stories in "Homer Price." A Proclamation from the Mayor regarding this event is issued dated April 23, 2002

    Roseland Reads Together, Sign, Roseland Free Public Library (Roseland, N.J.), 2002

    No full text
    Album chronicling the 30th Anniversary of the Roseland Library's Incorporation. The event was commemorated by a Borough-Wide reading activity. All families were invited to read the same book, "Homer Price" by Robert McCloskey. The festivities on May 11, 2002 at the Library included events from the stories in "Homer Price." A Proclamation from the Mayor regarding this event is issued dated April 23, 2002

    Labor Saving Devices, inspired by Homer Price," Display, Roseland Free Public Library (Roseland, N.J.)

    No full text
    Album chronicling the 30th Anniversary of the Roseland Library's Incorporation. The event was commemorated by a Borough-Wide reading activity. All families were invited to read the same book, "Homer Price" by Robert McCloskey. The festivities on May 11, 2002 at the Library included events from the stories in "Homer Price." A Proclamation from the Mayor regarding this event is issued dated April 23, 2002

    Labor Saving Devices, inspired by Homer Price," Display, Roseland Free Public Library (Roseland, N.J.)

    No full text
    Album chronicling the 30th Anniversary of the Roseland Library's Incorporation. The event was commemorated by a Borough-Wide reading activity. All families were invited to read the same book, "Homer Price" by Robert McCloskey. The festivities on May 11, 2002 at the Library included events from the stories in "Homer Price." A Proclamation from the Mayor regarding this event is issued dated April 23, 2002

    Enhancing the contribution of open and distance e-learning in higher education : implications for the central university of technology, Free State

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    Published ArticleThe aims of this article are to describe the findings of the author over the last decade regarding traditional distance education which eventually became Open and Distance E-Learning (ODEL) at the Central University of Technology, Free State (CUT) and secondly, the integration of Open Education Resources (OER) within ODEL. Up for debate in Perspectives in Education is the question whether ODEL and OER have not already stimulated a new constellation for higher education? After attending several international conferences of the International Organization for Open and Distance Education (lODE), the National Association for Open Distance Education of South Africa (NADEOSA), Higher Education Learning and Teaching Association of Southern Africa (HELTASA) as well as the South African Association for Research Development in Higher Education (SMRDHE), it became evident to the author that global trends forced a number of changes onto the South African higher education system. Subsequently, the CUT also had to reconsider the role of distance education within the Free State and Northern Cape provinces where it operates. In 2004 for example, students enrolled for distance education countrywide already constituted between 4% and 32% at traditional face-to-face universities while for universities of technology the figure was only 4,74% (CHE, 2004:185-186). However, universities of technology since expanded tremendously in using ODEL
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