• Corpus ID: 59405451

# Spanning closed walks with bounded maximum degrees of graphs on surfaces

@article{Hasanvand2017SpanningCW,
title={Spanning closed walks with bounded maximum degrees of graphs on surfaces},
author={Morteza Hasanvand},
journal={arXiv: Combinatorics},
year={2017}
}
Gao and Richter (1994) showed that every $3$-connected graph which embeds on the plane or the projective plane has a spanning closed walk meeting each vertex at most $2$ times. Brunet, Ellingham, Gao, Metzlar, and Richter (1995) extended this result to the torus and Klein bottle. Sanders and Zhao (2001) obtained a sharp result for higher surfaces by proving that every $3$-connected graph embeddable on a surface with Euler characteristic $\chi \le -46$ admits a spanning closed walk meeting each…

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