NDLI: Line-Polar Graphs: Characterization and Recognition

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Huang, Jing Churchley, Ross
Copyright Year	2011
Abstract	A graph is polar if its vertex set can be partitioned into A and B in such a way that A induces a complete multipartite graph and B induces a disjoint union of cliques (i.e., the complement of a complete multipartite graph). Polar graphs naturally generalize several classes of graphs such as bipartite, cobipartite, and split graphs. The problem of recognizing polar graphs is NP-complete in general. However, it has been shown to be polynomial for several classes of graphs, including cographs and chordal graphs. In this paper, we study the problem of recognizing graphs whose line graphs are polar. It turns out that the core part of this problem lies in determining whether the edge set of a graph admits a partition (A,B) so that A induces a P3-free subgraph (i.e., a matching) and B induces a P4-free subgraph. We give a structural characterization of such graphs. The characterization enables us to devise an O(n) time algorithm to solve the stated recognition problem.
Starting Page	1269
Ending Page	1284
Page Count	16
File Format	PDF
ISSN	08954801
DOI	10.1137/100789208
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	25
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-08-25
Access Restriction	Subscribed
Subject Keyword	monopolar partition Factorization, matching, partitioning, covering and packing line-monopolar graph structural characterization polar partition Structural characterization of families of graphs line-polar graph Graph algorithms linear time recognition algorithm
Content Type	Text
Resource Type	Article
Subject	Mathematics

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