A Generalization of Slightly Triangulated Graphs
نویسنده
چکیده
Maire introduced the class of those graphs without long holes, for which every induced subgraph possesses a vertex whose neighbourhood has no P4. Those graphs are called slightly triangulated graphs and are proven to be perfect in [14]. In this paper, we introduce a wider class of graphs, obtained by relaxing the neighbourhood condition. We also provide polynomial algorithms to recognize and to produce an optimal coloring of a subclass of slightly triangulated graphs.
منابع مشابه
Slightly triangulated graphs are perfect
A graph is triangulated if it has no chordless cycle with at least four vertices (8k 4; C k 6 6 G). These graphs have been generalized by R. Hayward with the weakly triangulated graphs (8k 5; C k ; C k 6 6 G). In this note we propose a new generalization of triangulated graphs. A graph G is slightly triangulated if it satisses the two following conditions : 1. G contains no chordless cycle with...
متن کاملOptimizing 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...
متن کاملA generalization of zero-divisor graphs
In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores
متن کاملFinding the maximum-weight induced k-partite subgraph of an i-triangulated graph
An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite...
متن کاملA generalization of Villarreal's result for unmixed tripartite graphs
In this paper we give a characterization of unmixed tripartite graphs under certain conditions which is a generalization of a result of Villarreal on bipartite graphs. For bipartite graphs two different characterizations were given by Ravindra and Villarreal. We show that these two characterizations imply each other.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999