Paul Gartside Max Pitz (11 results)

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  • Language: English

    Published by American Mathematical Society, US, 2024

    1470467844 / 9781470467845

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    Paperback. Condition: New. We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and Kühn with the topological theory of Eulerian continua defined as irreducible images of the circle, as proposed by Bula, Nikiel and Tymchatyn. First, we clarify the notion of an Eulerian space and establish that all competing definitions in the literature are in fact equivalent. Next, responding to an unsolved problem of Treybig and Ward from 1981, we formulate a combinatorial conjecture for characterising the Eulerian spaces, in a manner that naturally extends the characterisation for finite Eulerian graphs. Finally, we present far-reaching results in support of our conjecture which together subsume and extend all known results about the Eulerianity of infinite graphs and continua to date. In particular, we characterise all one-dimensional Eulerian spaces.…

  • Language: English

    Published by American Mathematical Society, 2024

    1470467844 / 9781470467845

    • Softcover

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    Paperback. Condition: Brand New. 86 pages. 7.01x0.77x10.00 inches. In Stock.

  • Language: English

    Published by Amer Mathematical Society, 2024

    1470467844 / 9781470467845

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  • Language: English

    Published by American Mathematical Society, 2024

    1470467844 / 9781470467845

    • Softcover

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  • Language: English

    Published by Amer Mathematical Society, 2024

    1470467844 / 9781470467845

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  • Language: English

    Published by Amer Mathematical Society, 2024

    1470467844 / 9781470467845

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  • Language: English

    Published by American Mathematical Society, 2024

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  • Language: English

    Published by Amer Mathematical Society, 2024

    1470467844 / 9781470467845

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  • Language: English

    Published by Amer Mathematical Society, 2024

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  • Language: English

    Published by Amer Mathematical Society, 2024

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  • Language: English

    Published by American Mathematical Society, US, 2024

    1470467844 / 9781470467845

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    Paperback. Condition: New. We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and Kühn with the topological theory of Eulerian continua defined as irreducible images of the circle, as proposed by Bula, Nikiel and Tymchatyn. First, we clarify the notion of an Eulerian space and establish that all competing definitions in the literature are in fact equivalent. Next, responding to an unsolved problem of Treybig and Ward from 1981, we formulate a combinatorial conjecture for characterising the Eulerian spaces, in a manner that naturally extends the characterisation for finite Eulerian graphs. Finally, we present far-reaching results in support of our conjecture which together subsume and extend all known results about the Eulerianity of infinite graphs and continua to date. In particular, we characterise all one-dimensional Eulerian spaces.…