3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian

Haitze J. Broersma, H.J. Veldman

Research output: Contribution to journalArticleAcademic

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Abstract

A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.
Original languageUndefined
Pages (from-to)399-407
JournalJournal of graph theory
Volume11
Issue number3
DOIs
Publication statusPublished - 1987

Keywords

  • IR-70828

Cite this

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abstract = "A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.",
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author = "Broersma, {Haitze J.} and H.J. Veldman",
year = "1987",
doi = "10.1002/jgt.3190110314",
language = "Undefined",
volume = "11",
pages = "399--407",
journal = "Journal of graph theory",
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publisher = "Wiley-Liss Inc.",
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3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian. / Broersma, Haitze J.; Veldman, H.J.

In: Journal of graph theory, Vol. 11, No. 3, 1987, p. 399-407.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - 3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian

AU - Broersma, Haitze J.

AU - Veldman, H.J.

PY - 1987

Y1 - 1987

N2 - A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.

AB - A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.

KW - IR-70828

U2 - 10.1002/jgt.3190110314

DO - 10.1002/jgt.3190110314

M3 - Article

VL - 11

SP - 399

EP - 407

JO - Journal of graph theory

JF - Journal of graph theory

SN - 0364-9024

IS - 3

ER -