NDLI: Split-Perfect Graphs: Characterizations and Algorithmic Use

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Split-Perfect Graphs: Characterizations and Algorithmic Use

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Brandstdt, Andreas Le, Van Bang
Copyright Year	2004
Abstract	Two graphs G and H with the same vertex set Vare P4 -isomorphic if every four vertices {a,b,c,d} \subseteq V$ induce a chordless path (denoted by P4 ) in G if and only if they induce a P4 in H. We call a graph split-perfect if it is P4 -isomorphic to a split graph (i.e., a graph being partitionable into a clique and a stable set). This paper characterizes the new class of split-perfect graphs using the concepts of homogeneous sets and p-connected graphs and leads to a linear time recognition algorithm for split-perfect graphs, as well as efficient algorithms for classical optimization problems on split-perfect graphs based on the primeval decomposition of graphs. The optimization results considerably extend previous ones on smaller classes such as P4 --sparse graphs, P4 -lite graphs, P4 --laden graphs, and (7,3)-graphs. Moreover, split-perfect graphs form a new subclass of brittle graphs containing the superbrittle graphs for which a new characterization is obtained leading to linear time recognition.
Starting Page	341
Ending Page	360
Page Count	20
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480100367676
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	17
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	$P_4$-structure of perfect graphs $P_4$-lite graphs perfectly orderable graphs Structural characterization of families of graphs good characterization $P_4$-sparse graphs brittle graphs Perfect graphs superbrittle graphs graphs with $P_4$-structure of split graphs perfect graphs primeval decomposition tree linear time recognition $P_4$-laden graphs Graph algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics

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