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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Disjoint paths, planarizing cycles, and
spanning walks


Author: Xingxing Yu
Journal: Trans. Amer. Math. Soc. 349 (1997), 1333-1358
MSC (1991): Primary 05C38, 05C10, 57M15
MathSciNet review: 1401533
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Abstract: We study the existence of certain disjoint paths in planar graphs and generalize a theorem of Thomassen on planarizing cycles in surfaces. Results are used to prove that every 5-connected triangulation of a surface with sufficiently large representativity is hamiltonian, thus verifying a conjecture of Thomassen. We also obtain results about spanning walks in graphs embedded in a surface with large representativity.


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Additional Information

Xingxing Yu
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Address at time of publication: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: yu@math.vanderbilt.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01830-8
PII: S 0002-9947(97)01830-8
Keywords: bridge, disjoint paths, embedding, Hamilton cycle, representativity, walk
Received by editor(s): August 20, 1993
Additional Notes: Partially supported by NSF grants DMS–9105173 and DMS–9301909
Article copyright: © Copyright 1997 American Mathematical Society