Triangulated graphs and the elimination process

Triangulated and Weakly Triangulated Graphs: Simpliciality in Vertices and Edges

Optimizing slightly triangulated graphs

Graphs is called slightly if it contaiw; no chordless cyck or more vertices and induced subgrapb has a vertex whose nellgnLoc1urnooCl contains no induced path on four verticf~S. These graphs triangulated graphs and appear naturally in the study of thf~ inhcrsection graphs of the maximal rectangles of trii::.tngulated graphs are perfect (in the sense of Berge). In this paper WI? present algorith...

Generating weakly triangulated graphs

We show that a graph is weakly triangulated, or weakly chordal, if and only if it can be generated by starting with a graph with no edges, and repeatedly adding an edge, so that the new edge is not the middle edge of any chordless path with four vertices. This is a corollary of results due to Sritharan and Spinrad, and Hayward, Hoo ang and Maaray, and a natural analogue of a theorem due to Fulk...

Monochromatic Paths and Triangulated Graphs

This paper considers two properties of graphs, one geometrical and one topolog-ical, and shows that they are strongly related. Let G be a graph with four distinguished and distinct vertices, w 1 ; w 2 ; b 1 ; b 2. Consider the two properties, T RI + (G) and M ON O(G), deened as follows. T RI + (G): There is a planar drawing of G such that: all 3-cycles of G are faces; all faces of G are triangl...

More characterizations of triangulated graphs

New characterizations of triangulated and cotriangulated graphs are presented. Cotriangulated graphs form a natural subclass of the class of strongly perfect graphs, and they are also characterized in terms of the shellability of some associated collection of sets. Finally, the notion of stability function of a graph is introduced, and it is proved that a graph is triangulated if and only if th...