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On the correspondence between tree representations of chordal and dually chordal graphs
(Elsevier, 2014-02)
Chordal graphs and their clique graphs (called dually chordal graphs) possess characteristic tree representations, namely, the clique tree and the compatible tree, respectively. The following problem is studied: given a ...
On basic chordal graphs and some of its subclasses
(Elsevier Science, 2016-09)
Basic chordal graphs arose when comparing clique trees of chordal graphs and compatible trees of dually chordal graphs. They were defined as those chordal graphs whose clique trees are exactly the compatible trees of its ...
Introducing subclasses of basic chordal graphs
(Elsevier Science, 2013-11)
Basic chordal graphs arose when comparing clique trees of chordal graphs and compatible trees of dually chordal graphs. They were defined as those chordal graphs whose clique trees are exactly the compatible trees of its ...
Neighborhood inclusion posets and tree representations for chordal and dually chordal graphs
(Elsevier Science, 2020-07)
This paper is motivated by the following problem: given the family ofclique trees of a chordal graph G, determine whether it is also the family of compatible trees of some dually chordal graph H. A relationship isestablished ...
Maxclique and unit disk characterizationsof strongly chordal graphs
(University of Zielona Gora, 2014-07)
Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations ...