Open AccessOn the structure of plane graphs of minimum face size 5
Author(s) -
Tomáš Madaras
Publication year - 2004
Publication title -
discussiones mathematicae graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.476
H-Index - 19
eISSN - 2083-5892
pISSN - 1234-3099
DOI - 10.7151/dmgt.1239
Subject(s) - mathematics , combinatorics , face (sociological concept) , plane (geometry) , discrete mathematics , geometry , sociology , social science
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 K1,3 and we present a structural result concerning the existence of a pair of adjacent faces with degree– bounded vertices.
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