A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected

Xiaoyun Lu; Douglas B. West

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 3, page 555-564
  • ISSN: 2083-5892

Abstract

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We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.

How to cite

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Xiaoyun Lu, and Douglas B. West. "A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected." Discussiones Mathematicae Graph Theory 36.3 (2016): 555-564. <http://eudml.org/doc/285916>.

@article{XiaoyunLu2016,
abstract = {We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.},
author = {Xiaoyun Lu, Douglas B. West},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {4-connected planar graph; Hamiltonian-connected; Tutte-path},
language = {eng},
number = {3},
pages = {555-564},
title = {A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected},
url = {http://eudml.org/doc/285916},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Xiaoyun Lu
AU - Douglas B. West
TI - A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 3
SP - 555
EP - 564
AB - We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.
LA - eng
KW - 4-connected planar graph; Hamiltonian-connected; Tutte-path
UR - http://eudml.org/doc/285916
ER -

References

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  1. [1] C. Thomassen, A theorem on paths in planar graphs, J. Graph Theory 7 (1983) 169-176. doi:10.1002/jgt.3190070205[Crossref] Zbl0515.05040
  2. [2] W.T. Tutte, A theorem on planar graphs, Trans. Amer. Math. Soc. 82 (1956) 99-116. doi:10.1090/S0002-9947-1956-0081471-8[Crossref] Zbl0070.18403
  3. [3] H. Whitney, A theorem on graphs, Ann. of Math. 32 (1931) 378-390. doi:10.2307/1968197[Crossref] Zbl0002.16101

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