Spanning trees in 3-connected K3,t-minor-free graphs

Katsuhiro Ota; Kenta Ozeki

doi:10.1016/j.endm.2009.07.024

Spanning trees in 3-connected K_3,t-minor-free graphs

Katsuhiro Ota, Kenta Ozeki

Department of Mathematics

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

2 Citations (Scopus)

Abstract

Barnette proved that every 3-connected planar graph has a 3-tree, where a 3-tree is a spanning tree whose maximum degree is at most three. In this paper, we consider an improvement of Barnette's result for the direction of K_{3, t}-minor-free graphs. Note that any planar graph is K_{3, 3}-minor-free. Actually, we show that for an even integer t ≥ 3, any 3-connected K_{3, t} -minor-free graph has a (t - 1)-tree.

Original language	English
Pages (from-to)	145-149
Number of pages	5
Journal	Electronic Notes in Discrete Mathematics
Volume	34
DOIs	https://doi.org/10.1016/j.endm.2009.07.024
Publication status	Published - 2009 Aug 1

Keywords

K-minor-free graphs
Planar graphs
Spanning tree

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.endm.2009.07.024

Cite this

@article{d09827825cac4e52a35c3055e1b874f3,

title = "Spanning trees in 3-connected K3,t-minor-free graphs",

abstract = "Barnette proved that every 3-connected planar graph has a 3-tree, where a 3-tree is a spanning tree whose maximum degree is at most three. In this paper, we consider an improvement of Barnette's result for the direction of K3, t-minor-free graphs. Note that any planar graph is K3, 3-minor-free. Actually, we show that for an even integer t ≥ 3, any 3-connected K3, t -minor-free graph has a (t - 1)-tree.",

keywords = "K-minor-free graphs, Planar graphs, Spanning tree",

author = "Katsuhiro Ota and Kenta Ozeki",

year = "2009",

month = aug,

day = "1",

doi = "10.1016/j.endm.2009.07.024",

language = "English",

volume = "34",

pages = "145--149",

journal = "Electronic Notes in Discrete Mathematics",

issn = "1571-0653",

publisher = "Elsevier",

}

TY - JOUR

T1 - Spanning trees in 3-connected K3,t-minor-free graphs

AU - Ota, Katsuhiro

AU - Ozeki, Kenta

PY - 2009/8/1

Y1 - 2009/8/1

N2 - Barnette proved that every 3-connected planar graph has a 3-tree, where a 3-tree is a spanning tree whose maximum degree is at most three. In this paper, we consider an improvement of Barnette's result for the direction of K3, t-minor-free graphs. Note that any planar graph is K3, 3-minor-free. Actually, we show that for an even integer t ≥ 3, any 3-connected K3, t -minor-free graph has a (t - 1)-tree.

AB - Barnette proved that every 3-connected planar graph has a 3-tree, where a 3-tree is a spanning tree whose maximum degree is at most three. In this paper, we consider an improvement of Barnette's result for the direction of K3, t-minor-free graphs. Note that any planar graph is K3, 3-minor-free. Actually, we show that for an even integer t ≥ 3, any 3-connected K3, t -minor-free graph has a (t - 1)-tree.

KW - K-minor-free graphs

KW - Planar graphs

KW - Spanning tree

UR - http://www.scopus.com/inward/record.url?scp=67651165182&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67651165182&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2009.07.024

DO - 10.1016/j.endm.2009.07.024

M3 - Article

AN - SCOPUS:67651165182

SN - 1571-0653

VL - 34

SP - 145

EP - 149

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -