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

DOI:
https://doi.org/10.1090/S0002-9947-97-01830-8

MathSciNet review:
1401533

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-97-01830-8

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