A class of planar well‐covered graphs with girth four
作者:
Michael R. Pinter,
期刊:
Journal of Graph Theory
(WILEY Available online 1995)
卷期:
Volume 19,
issue 1
页码: 69-81
ISSN:0364-9024
年代: 1995
DOI:10.1002/jgt.3190190108
出版商: Wiley Subscription Services, Inc., A Wiley Company
数据来源: WILEY
摘要:
AbstractA well‐covered graph is a graph in which every maximal independent set is a maximum independent set; Plummer introduced the concept in a 1970 paper. The notion of a 1‐well‐covered graph was introduced by Staples in her 1975 dissertation: a well‐covered graphGis 1‐well‐covered if and only ifG‐vis also well covered for every pointvinG. Except forK2andC5, every 1‐well‐covered graph contains triangles or 4‐cycles. We show that all planar 1‐well‐covered graphs of girth 4 belong to a specific infinite family, and we give a characterization of this family. © 1
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