NDLI: On the Complexity of Finding a Sun in a Graph

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hong, Chnh T.
Copyright Year	2010
Abstract	The sun is the graph obtained from a cycle of length even and at least six by adding edges to make the even-indexed vertices pairwise adjacent. Suns play an important role in the study of strongly chordal graphs. A graph is chordal if it does not contain an induced cycle of length at least four. A graph is strongly chordal if it is chordal and every even cycle has a chord joining vertices whose distance on the cycle is odd. Farber proved that a graph is strongly chordal if and only if it is chordal and contains no induced suns. There are well known polynomial-time algorithms for recognizing a sun in a chordal graph. Recently, polynomial-time algorithms for finding a sun for a larger class of graphs, the so-called HHD-free graphs (graphs containing no house, hole, or domino), have been discovered. In this paper, we prove the problem of deciding whether an arbitrary graph contains a sun is NP-complete.
Starting Page	2156
Ending Page	2162
Page Count	7
File Format	PDF
ISSN	08954801
DOI	10.1137/080729281
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	23
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-01-22
Access Restriction	Subscribed
Subject Keyword	Analysis of algorithms and problem complexity chordal graph strongly chordal graph sun
Content Type	Text
Resource Type	Article
Subject	Mathematics

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On the Complexity of Finding a Sun in a Graph