The hamiltonian index of a graph and its branch-bonds

Liming Xiong; H. J. Broersma; Xueliang Li; Ming Chu Li

doi:10.1016/j.disc.2004.01.018

The hamiltonian index of a graph and its branch-bonds

Liming Xiong^*, H. J. Broersma, Xueliang Li, Ming Chu Li

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph L^m(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G)≥2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic.

Original language	English
Pages (from-to)	279-288
Number of pages	10
Journal	Discrete Mathematics
Volume	285
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.01.018
Publication status	Published - 6 Aug 2004

Keywords

Branch-bond
Hamiltonian index
Iterated line graph
Reduction method

Access to Document

10.1016/j.disc.2004.01.018

Cite this

@article{a9da0bec9b514ccf81e8edbe4b965fb9,

title = "The hamiltonian index of a graph and its branch-bonds",

abstract = "Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G)≥2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic.",

keywords = "Branch-bond, Hamiltonian index, Iterated line graph, Reduction method",

author = "Liming Xiong and Broersma, {H. J.} and Xueliang Li and Li, {Ming Chu}",

year = "2004",

month = aug,

day = "6",

doi = "10.1016/j.disc.2004.01.018",

language = "English",

volume = "285",

pages = "279--288",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "1-3",

}

TY - JOUR

T1 - The hamiltonian index of a graph and its branch-bonds

AU - Xiong, Liming

AU - Broersma, H. J.

AU - Li, Xueliang

AU - Li, Ming Chu

PY - 2004/8/6

Y1 - 2004/8/6

N2 - Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G)≥2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic.

AB - Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G)≥2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic.

KW - Branch-bond

KW - Hamiltonian index

KW - Iterated line graph

KW - Reduction method

UR - http://www.scopus.com/inward/record.url?scp=3142639201&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2004.01.018

DO - 10.1016/j.disc.2004.01.018

M3 - Article

AN - SCOPUS:3142639201

SN - 0012-365X

VL - 285

SP - 279

EP - 288

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

The hamiltonian index of a graph and its branch-bonds

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this