Eulerian Spaces

Paul Gartside, Max Pitz (Autoren)

Buch | Softcover

86 Seiten

2024
American Mathematical Society (Verlag)
978-1-4704-6784-5 (ISBN)

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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.

Paul Gartside, University of Pittsburgh, Pennsylvania. Max Pitz, Universitat Hamburg, Germany.

Erscheinungsdatum	02.02.2024
Reihe/Serie	Memoirs of the American Mathematical Society ; Volume: 292 Number: 1456
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	272 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-6784-4 / 1470467844
ISBN-13	978-1-4704-6784-5 / 9781470467845
Zustand	Neuware