Tank-ring factors in supereulerian claw-free graphs

MingChu Li; Lifeng Yuan; He Jiang; Bing Liu; Haitze J. Broersma

doi:10.1007/s00373-011-1117-z

Tank-ring factors in supereulerian claw-free graphs

MingChu Li, Lifeng Yuan, He Jiang, Bing Liu, Haitze J. Broersma

Discrete Mathematics and Mathematical Programming

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

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Abstract

A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of G − C contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.

Original language	Undefined
Pages (from-to)	599-608
Number of pages	10
Journal	Graphs and combinatorics
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s00373-011-1117-z
Publication status	Published - 2013

Keywords

MSC-05C
EWI-23369
Claw-free graph
IR-86130
Hourglass property
METIS-297653
Hamiltonian graph

Access to Document

10.1007/s00373-011-1117-z

http://eprints.eemcs.utwente.nl/secure2/23369/01/10.1007_s00373-011-1117-z.pdf

Cite this

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title = "Tank-ring factors in supereulerian claw-free graphs",

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AU - Li, MingChu

AU - Yuan, Lifeng

AU - Jiang, He

AU - Liu, Bing

AU - Broersma, Haitze J.

N1 - eemcs-eprint-23369

PY - 2013

Y1 - 2013

N2 - A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of G − C contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.

AB - A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of G − C contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.

KW - MSC-05C

KW - EWI-23369

KW - Claw-free graph

KW - IR-86130

KW - Hourglass property

KW - METIS-297653

KW - Hamiltonian graph

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DO - 10.1007/s00373-011-1117-z

M3 - Article

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IS - 3

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