# On the structure of plane graphs of minimum face size 5

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 3, page 403-411
- ISSN: 2083-5892

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topTomás Madaras. "On the structure of plane graphs of minimum face size 5." Discussiones Mathematicae Graph Theory 24.3 (2004): 403-411. <http://eudml.org/doc/270681>.

@article{TomásMadaras2004,

abstract = {A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star $K_\{1,3\}$ and we present a structural result concerning the existence of a pair of adjacent faces with degree-bounded vertices.},

author = {Tomás Madaras},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {plane graph; light graph; face size},

language = {eng},

number = {3},

pages = {403-411},

title = {On the structure of plane graphs of minimum face size 5},

url = {http://eudml.org/doc/270681},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Tomás Madaras

TI - On the structure of plane graphs of minimum face size 5

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 3

SP - 403

EP - 411

AB - A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star $K_{1,3}$ and we present a structural result concerning the existence of a pair of adjacent faces with degree-bounded vertices.

LA - eng

KW - plane graph; light graph; face size

UR - http://eudml.org/doc/270681

ER -

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