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Chordal probe graphs

Authors: Golumbic, Martin Charles; Lipshteyn, Marina;

Chordal probe graphs

Abstract

A graph \(G=(V, E)\) is a chordal probe graph if there exists a partition \(V=P\cup N\) with a stable set \(N\) and a completion \(E'\subseteq\{uv : u\not= v\in N\}\) such that the graph \((V, E\cup E')\) is a chordal graph. Chordal probe graphs generalize probe interval graphs introduced by P. Zhang; see also [\textit{F. R. McMorris, C. Wang} and \textit{P. Zhang}, Discrete Appl. Math. 88, 315--324 (1998; Zbl 0918.05087)]. Among other initial results on chordal probe graphs, the authors prove that chordal probe graphs which are also weakly chordal can be recognized in \(O(m^2)\) time where a partition \(P\cup N\) is given or not, and \(m\) is the number of edges. The complexity of recognizing chordal probe graphs in general is still open, even in the partitioned version.

Related Organizations
Keywords

Probe graphs, Chordal graphs, Applied Mathematics, Interval graphs, Discrete Mathematics and Combinatorics, interval graphs, Structural characterization of families of graphs, chordal graphs, probe graphs

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
33
Top 10%
Top 10%
Top 10%
hybrid